chess engines

They calculate a lot of positions per second and render a mostly reliable evaluation for all the legal moves. The evaluation is given in centi-pawns which means 100ths of a pawn. For example an evaluation like 0.50 would a half pawn advantage. Obviously isn't not possible to literally have half a pawn, but this is how it expresses other factors like space, piece activity, king safety, etc. It considers all that and outputs just 1 number.

Even though it considers each legal move in the current position of course people are generally only interested in what the engine thinks is the best (or near best) move (sometimes near beat because the "best" move according to the engine is sometimes impractical).

Also, of course, it can't continue to consider every legal move as it calculates further and further. Moves that seem to be leading nowhere are ignored.

 First of all, to use one you'll need a separate piece of software that allows you to use it.

E.g. arena http://www.playwitharena.com
or scid http://scid.sourceforge.net

You can see list of engines here:

http://www.computerchess.org.uk/ccrl/4040/

And e.g. download stockfish here

https://stockfishchess.org/download/

Engines are mostly useful to find your biggest tactical oversights. They can criticize every little move too, but that doesn't really help you play any better, so when using one just pay attention to the big swings in evaluation.

And more importantly, the way to improve isn't really by using engines (although they can help of course). More important for improvement is playing long games and reading books.

I own and use both Fritz 16, Chessbase 14, Chess Ultra, and Lucas Chess.

I'm not a great one to give advice, because my rating is relatively low (USCF 1438 Over the board). I'm also pathetic at blitz. But I can at least answer some things about how you use them.

1) There is a lot of advice out there that to really improve, you need to play slower games and not blitz. Finding people to play slow games online can be difficult. If you have a  chess engine like Fritz 16, it is trivial. And you can adjust its level of play to your desired strength of opponent. For example, I often play 45 minute or 75 minute games against Fritz.

2) There is a lot of advice out there that says you should annotate your games after you play, especially if you lose. Fritz has a surprisingly good database that stores your games. And it is possible to go in and annotate your games after you have played. After you have annotated the game, you can also run the chess engine against the game to find things you may have missed. It will insert its comments into the game as well.

3) There is also a lot of advice that says you should play over games by Grandmasters. Fritz 16 comes with a database of over 1 million games. Furthermore, 10s of thousands of them are annotated already. This is a VERY convenient way to play over games.

4) There are also some training features built in. For example, you can practice openings against it.

5) It also has features that will let you know what it considers to be good and bad moves for a piece before you actually move it. This has some training value, but can also, in my opinion, be harmful if used wrong. I personally have taken to turning it off recently. Likewise it has a mode where it will alert you there is a tactical shot in the position. It will then tell you if you found it or missed it.

Now for some downsides - it is NOT the same as playing someone over the board. Computers play somewhat differently than people do. I find playing an a person over the board to be a somewhat more intense experience (I find playing over the board is also more intense than playing online). Also, although the can be set to play at a strength you specify, the way the make errors is rather different than playing an actual person.

I think Fritz 16 is well worth getting. If you don't want to spend the money, you could also look into Lucas Chess. It is free, and comes with some very good chess engines built in. The interface is not as polished (in my opinion) but it is still quite usable.

Well, a chess engine is a piece of software that can calculate many chess moves. Top grandmasters use these engines to find the best moves, then they memorize them and play them in their games.