"The econony needs x workers of profession y". What does it mean and how is it derived? I keep hearing that there is not enough of some specialists in economy which is followed by some number. Here's an example:

http://www.computerweekly.com/news/2240205466/Economy-needs-300000-digital-workers-by-2020-to-reach-full-potential


  Economy needs 300,000 digital workers by 2020 to reach full potential


How is this derived? Is it reasonable?

Job market is regulated by supply and demand. To follow the example of "digital worker" - I believe that many, for example, engineers could change their job profile to become "digital workers", but in that case engineers would be suddenly in higher demand as well.

We can say that janitor contributes x to GDP and database administrator contributes y and because y > x, we need more db administrators than janitors, but in reality we need exactly the current number of janitors given their market price and we need exactly the current number of database administrators given their market price.

Also I can think of a question "How many digital workers do we need to inject into economy by 2020 so that the number of digital workers on the market in 2021 will be the same as in 2020?" and the answer could be 300 000. But how to calculate it without being simplistic?

To reiterate: what does it mean that we need x new professionals and how to calculate it?
Full-factor employment GDP (referring not only to labor but also to capital and any other factor), results from existing factor stock interacting with production technology. It is a (quasi) "engineering" relationship, not an economic one. 

It says "if all labor and all capital were employed, given technology, output will reach its feasible maximum". It does not say that it is an optimal level in any sense. It does not allow for labor-leisure choice or lock-out (idle capital). It does not take into account whether current markets actually clear (or not). 

Still we informally accept that "more is better" so we do examine what would it take to reach this feasible maximum, or how economic interactions, incentives, institutions etc may or may not lead us to such a full-factor employment GDP.

In the case examined by the question here, it appears that an expert body has identified an "engineering" mismatch in the composition of the labor force. Namely, this body of researchers has estimated the required compostion of the labor force that can lead the economy to "feasible maximum GDP"-and then found that the actual composition does not align with the former.

As to how one can indeed estimate such "required compositions" of the labor force, well, this is too technical to go into here, but it can be done.