Chess Piece Relative Values
In chess, pieces are constantly being exchanged. But not all exchanges are equal. Just because you took one of your opponent's pieces and he took one of your pieces does not necessarily mean that everything came out even, because different pieces have different powers. Simply put, some pieces are worth more than others.
The worth of all your pieces together is commonly referred to as your "material." If your total worth is more than your opponent's you are said to be "ahead in material" or "up in material" whereas he is "behind in material" or "down in material." If you make a trade where you give up a more powerful piece for a less powerful piece, you are said to have "lost material" while your opponent has "gained material."
So how do you know what each piece is worth? There are conventional values, worked out through experience and testing, that have become commonly agreed upon as representing the strength of the various pieces. Taking the pawn as the basic unit and assigning it a value of 1 point, the conventional values are as follows:
It is important to note that these values are purely for your own consideration. There is no such thing as "scoring points" in chess and at no time during a game will you ever stop and count piece values to determine a winner. They are simply a useful metric for evaluating potential exchanges, and determing what constitutes a rough "balance of power" when formulating a strategy.
It's also worth noting that although these are the most commonly used values, some sources will give slightly different ones. In particular the value for the bishop is often adjusted to be slightly higher than the knight, and some players prefer assigning the queen 10 points rather than 9. But for simplicity, it's best to start with the values given here. (As a sidenote this implies that knights and bishops have equal value, and while this is a complex topic I believe that beginners should treat them as equal).
So how do we actually use these values? It's pretty simple really. Suppose your opponent has just moved his pawn to attack your knight. Should you let him take your knight, if in return you can take the pawn on your next move? No! Because a pawn is worth 1 point and a knight is worth 3 points, making that trade will result in a definite disadvantage.
In fact most players learn very early on that a knight is worth more than a pawn. But how much more? What about a knight for two pawns? And what about more unusual trades, such as a rook for two knights or a queen for two rooks? The real utility of the point system is that it does a pretty good job at answering those questions in a very simple objective way.
Let's see...since a knight is worth 3 points, a knight for two pawns is still a bad trade. We would need to get three pawns in return for the knight in order for it to be even. And if we could get four pawns for it, we would actually come out ahead. Those are the conclusions based on the point system, and indeed they have been confirmed by decades of experience -- a knight (or bishop) is worth approximately three pawns.
How about that rook for two knights trade? A pretty good deal as it turns out, as two knights (6 points) are worth slightly more than a rook (5 points). Similarly with a queen for two rooks -- the rooks (10 points) are worth slightly more than the queen (9 points). Again this corresponds well with actual experience, which has shown that generally speaking two knights (or two bishops or knight+bishop) are worth more than a rook, and two rooks are a bit better than a queen.
Of course all of this really only applies when considering overall long-term potential in what might be called a "stable" position. If a knight is about the deliver checkmate it is obviously worth more in that moment than a queen, or a whole army for that matter. And if a player has a two-move checkmate sequence which starts with giving up his queen for a pawn, he can hardly be said to have made a bad trade. But those are exceptional circumstances and not the normal conditions we're talking about here. When dealing with typical positions, you should have these point values committed to memory and use them to evaluate every exchange opportunity that arises.