There are four primary means of evaluating the strength of the two relative positions in a single game of chess:1 pawn structure, material, space, and initiative. I would argue that, while important to learn and essential to execute an opening, pawn structure empowers the triad of other characteristics rather than stands up an equal before them. Material, space, and initiative are bound by a flexible triangle in which a decisive advantage of any one category might exert pressure on the opponent to sacrifice even-play in a second category to gain equity in the first.
The technical terms:
- Material - the pieces on the board, assigned relative value
- Space - the sum of all squares on the board which are controlled by, defended, or being attacked by your material
- Initiative - also called 'tempo', this is the knives' edge between attacking and defending. White begins the game with the initiative, and keeps it until lost. The initiative is maintained by selecting moves which the opponent must address and defend against or suffer immediate consequences. Manners by which initiative might be maintained include: a double check, a forced check, a forced attack on a major piece, a fork check, a fork of a major piece, advancing a passed pawn, attacking an undefended piece, or the threat of any such move. The old chestnut: "What's the most powerful move in chess?"2
The relative values of each piece of material are well-known and generally accepted. Below are the values every beginning player learns, which help reinforce the relative 'strength' of each piece and also aid in evaluating material trades and liquidations.
Beyond material it quickly becomes murkier to quantify the 'space' and 'initiative' each player possesses. Do you count up how many squares you control? How many squares your opponent controls? Or is it the difference between your squares and your opponent's? Do you count up your total number of legal moves (seeking a maximum), count up your opponents total number of legal moves (seeking a minimum), or is it a difference between the two (again seeking a maximum)? And how is the human mind supposed to juggle this overload in a perfect-information game? Time control is on and the flag is burning, after all...
Enter the centipawn.
Defined as 1/100th of the material value of a single pawn, the centipawn is a unit of analytical currency to evaluate the relative strength between the move a player made and the best move available given the position they were given3. The best move available is defined by the chess analysis engine of your choice (Stockfish is the only open source chess engine as of writing, whereas Komodo has recently won the world AI title, Houdini is mere points of ELO rating behind and still stronger than any human player, and Google's AlphaZero remains a proprietary secret after thoroughly trouncing Stockfish in an 100 match test). As such - should the human player make the best possible move for the position, they will lose 0 centipawn. It does not matter if they play g3 or NxQ - so long as the move was the best one it is evaluated at a 0 centipawn loss. Likewise, if a player moved NxQ when another piece could have delivered checkmate, that would be evaluated at a significant centipawn loss.
A player's average centipawn loss, for a given match, is the arithmetical mean (average) of centipawn loss per move. The sum of centipawn loss divided by the total number of moves in the game will yield the final result.
The best players in the world are so accurate that their games are in the realm of 10-15 average centipawn loss. "Inaccuracies" and "mistakes" get labeled for moves which have 20-50 centipawn loss, and anything over 50 centipawn loss is a "blunder". Average players (1200-1800 ELO) will have a wide range of 60-97 average centipawn loss4, with higher loss values against stronger players and during matches in which they were generally outplayed.
Footnotes
1 - Wikipedia, "Initiative", accessed 2018-09-04.
2 - Answer: The next one.
3 - Lichess, "What is average centipawn loss?", accessed 2018-09-04.
4 - Chess-db, "ACL vs ELO scatter plot", accessed 2018-09-19.