Between the lines, I learnt at least three new things...

Thanks for your essay. Here are a few comments.

Word Choice/Word Form/Usage

• Today’s economical situation → Today’s economic situation
• Today’s economic situation leaves no doubt for both parents to go out to work → Today’s economic situation forces both parents to go out to work
• In any case the effects of this behavior on children is of a great importance → This has a major effect on children.

We could put both sentences together:

With both mothers and fathers working, some children find themselves forgotten or overlooked.

Thesis

You wrote:

In this essay I will support the fact that how this phenomenon benefits the children economically, mentally and socially.

Specifiy. What phenomenon? Avoid all ambiguity and make every sentence relevant to the topic. Here’s one possible rewrite:

In this essay I will describe how having both parents working can help the child economically, mentally and socially.

Paragraph Two

In your topic sentence you wrote:

Many people are more concerned about childhood depression or family imbalance as some disadvantages of this situation. (17 words)

Which situation?  Again the reference is unclear. To get a good mark in Coherence and Cohesion (see here in the official descriptors for IELTS Task 2 Writing (public version) you need to make pronouns and links and reference very clear.

Another problem is the word ‘more’  - more than what? It’s a comparison word, so the reader looks for something to compare with.

Let’s rewrite. Let’s leave out the unnecessary ‘people’:

There can be problems if both parents work. (8 words)  

OR
Having both parents work outside the home can lead to several problems. (12 words) First, …

You wrote:

One serious threat in such as situation is that parents might gradually forget the most basic and genuine need of their children which is sentimental care.

‘Such a situation'? Specify! Don’t make the reader think.

First, of all, the most basic need of a child is love and care.  

OR   

First of all, children need love and care.

Now you can follow this with your sentence: “Simply, children might feel forgotten while both parents are busy with their daily work life.”

Paragraph Two: Idea 2

You wrote:

Moreover, many people may suffer from family imbalance which is due to the fact that they cannot harmonize their work and life together. This is a situation which directly degrade a child’s life. As a wost case example, I can say such an event may lead to parental separation eventually which has a huge impact on a child’s life.

I’m not happy with this idea. I really am not sure what you mean. How will this ‘degrade’ the child’s life? Who are ‘the people’ in the first sentence. What does 'such an event' refer to? Keep going forward and don't make the reader remember: keep references clear.  I sort of get your idea, but it needs to be simpler and clearer. Why would parents divorce? How can work and life be 'harmonized'?

But you still only have TWO ideas in Paragraph Two. Three is better – much better, in fact. Don’t start to write until you have SIX ideas (three for, three against), in the same way you would not start to fly unless you had enough gas in your airplane’s fuel tank.

You wrote:

However, I think most of mentioned situations can be moderated if parents act wisely.

The word ‘mentioned’ makes the reader go back. Don’t make the reader go back. Keep going forward. Don’t use the words ‘latter’, ‘former,’ ‘respectively’, ‘aforementioned,’ ‘below,’ ‘above,’ or ‘hitherto.’ The reader is a goldfish. Just guide him or her gently along from the start to the end of your essay in one nice straight line. Don’t ask your reader to remember anything or to think what went before.

Word Choice

I put the essay into the link at Textalyser.net (see at the top of the page, under Useful Links.)

• Word             Occurrences
• children        10
• parents        10
• work            7
• family          6
• situation       6

You’ve used the word ‘situation’ 6 times. It's a vague word. What else could you use? (You’ve used ‘condition’ as well, which is another word I hate. It’s meaningless!)

You wrote :

As a result they can put their children in a better social condition. For example parents can now afford to send their children to language schools which is a result of good family financial condition.

Here's a rewrite:

As a result, parents can now afford to send their children to better schools.

Shorten/Simplify

You wrote:

Another advantage of this situation is that children can mentally learn that work is an important part of life. Therefore, they intuitively repeat their parents’ pattern when they grow up, so they can pay it forward to their next generations. (40 words)

Aah! ‘Situation’ again!  At least you used the word ‘pattern’ in the following sentence.  Let’s rewrite:

When parents work, children mentally learn that work is an important part of life. Therefore, they intuitively repeat their parents’ pattern when they grow up, with their own children.  (29 words)

Paragraph Three, Idea Three:

You wrote:

Last but not least, children can also take benefit of that socially because they have been grown up in a family in which both parents were socialized.

I’m not clear what you mean here by ‘socially’ or ‘socialized.’ I think it would come under Lexical Resource under “inappropriate word choice,”  or perhaps under Task Response as an idea “not fully developed.”  Can you let us know here what you mean?

Conclusion: No New Information

Your conclusion is OK. However, you have some new information in the last sentence, about benefits for parents. What are these? Try not to have  new information in your conclusion.

Overall

Try to eliminate vague or empty words and phrases like ‘condition,’ ‘situation,’ ‘of great importance.’ Keep pronoun references clear. Avoid “this phenomenon” or “this situation” and be careful even with “this.”

Reduce sentence length. Try to have short topic sentences so that you and the reader are reminded of what your paragraph is about .

Have three ideas, not two, for each paragraph.  Have a clear specific example for each. Do you know families which stay home? Where both parents work? Which divorced as a result of working too hard? The IELTS essay prompt asks you to give examples from your knowledge and experience. Don't be afraid to give short examples.

In today's competitive world, many families find it necessary for both parents to go out to work. While some say the children in these families benefit from the additional income, others feel they lack support because of their parents' absence.
Give reasons for your answer and include any relevant examples from your own knowledge or experience.

    Today’s economical situation leaves no doubt for both parents to go out to work. In any case the effects of this behavior on children is of a great importance. In this essay I will support the fact that how this phenomenon benefits the children economically, mentally and socially.

    Many people are more concerned about childhood depression or family imbalance as some disadvantages of this situation. One serious threat in such as situation is that parents might gradually forget the most basic and genuine need of their children which is sentimental care. In a simple word, children might be forgotten while both parents are busy with their daily work life. Moreover, many people may suffer from family imbalance which is due to the fact that they cannot harmonize their work and life together. This is a situation which directly degrade a child’s life. As a wost case example, I can say such an event may lead to parental separation eventually which has a huge impact on a child’s life. However, I think most of mentioned situations can be moderated if parents act wisely.

    I believe that parents can make more money and bring more prosperity for the whole family if they both work. As a result they can put their children in a better social condition. For example parents can now afford to send their children to language schools which is a result of good family financial condition. Another advantage of this situation is that children can mentally learn that work is an important part of life. Therefore, they intuitively repeat their parents’ pattern when they grow up, so they can pay it forward to their next generations. Last but not least, children can also take benefit of that socially because they have been grown up in a family in which both parents were socialized.

    In conclusion, I think the idea of both parents attend in professional work brings more advantages to the children in contrast to its flaws. Financial situation of the whole family will be improved, children can learn hard-work from their parents and also it has many benefits for the parents themselves.