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How to analyze your games with a chess engine?

A chess engine is a computer program that analyses chess positions and makes decisions on the best chess moves.
Chess engines (computer programs) use the standard notation to indicate who is better off (White or Black) in a given position using numbers.
A positive ("+") number means that White's position is better; conversely, a negative ("-") number means things look better for Black. 
However, the evaluation is not just about material currently on the board; computer analysis also looks ahead, factoring in positional aspects and tactical possibilities.
So, if the evaluation is +1.25, it means that White is ahead by 1.25 pawns (or "points"). (In other words, White has an advantage which is roughly equivalent to 1.25 pawns worth of material.)
Likewise, if the evaluation is -3.00, then Black is better - and Black's advantage is about the same as having an extra Bishop or Knight!
Sometimes, near the end of the game, you might see an evaluation like +M2: bad news if you're playing Black... This means White can force checkmate in two moves!