Equalize - What does it really mean? We often read or hear in books or video tutorials the following: "With this move, Black can equalize!". Some authors give 15-move or 20-move variations of some openings (e.g. Caro-Kann, Slav, Semi-Slav), then suddenly stop the explanation saying "...and Black managed to equalize".

Now, does "equalize" mean that Black should aim for "draw" at the start of the game? Should Black keep trying to "equalize" or "playing for draw" and wait for White to blunder then only star to think about how to win?

Does "equalize" mean that Black should try to exchange queens as early as possible?

Thanks!
This is a good question, because equality in chess is a tricky concept. 

From a theoretical point of view there are only three evaluations of position: "White is winning", "black is winning" and "it's a draw". So, when we talk about white being better or black having a "slight pull", these evaluations are heuristics that mirror our experience of who is having the better practical chances and by what degree. 

This also means that evaluations of the same position by different players can be quite different and often it is difficult to decide who is "more right". 

So, when an author declares, that black has equalised, he means that he considers black's chances to not be worse any more. This doesn't say anything about the nature of the position. For example some GMs would argue that in the king's gambit, after 1.e4 e5 2.f4 ef black has already equalised. But obviously the position isn't drawish in the least, there is still a big fight ahead. 

The idea that "trying to equalise first" is the same as "playing for a draw", comes from the fact, that it is often easiest to equalise by careful simplification. So there is a slightly artificial dichotomy between "trying to equalise first" and "going for a sharp fight". I call it slightly artificial because nowadays, especially among top players, the easiest way to equalise is often to go for the sharpest, most forcing lines.

As for what you should do: In my experience you should always try to develop counterplay, even if you are completely happy with a draw. If you can create even a slight initiative it is usually not difficult to exchange into a completely equal and drawish position. Whether exchanging queens should be your goal, depends entirely on the position.

In the end, how much risk you take is completely your decision. Some players try to go for the win straight away, even with black. Others want to play with the draw in hand, especially with white.