The number under the board is measured in pawns. Plus one point zero means the engine thinks White stands as well as he would with one extra pawn and everything else equal. Minus two point five says Black is two and a half pawns better. Zero point zero zero says neither side has anything.
A centipawn is one hundredth of that unit, so a score of +0.35 is thirty-five centipawns and a score of +1.00 is a hundred. Engines work in centipawns internally and the interface divides by a hundred before showing you the figure.
The scale, roughly
Nothing on the scale is exact, but it is easier to read once you attach real things to it. About one is a pawn. About three is a knight or bishop. Five is a rook, nine is a queen. Half a point is roughly the value of a safe extra move, the bishop pair, or a rook on the only open file.
Below about 0.3 there is nothing to talk about. The starting position, before anybody has touched a piece, sits at roughly +0.2 for having the first move, and no game was ever won with that.
Where the number stops meaning material
Here is a bishop and a pawn against nothing, and every engine on earth calls it 0.00.
8 
5 The pawn queens on h8. That square is dark, the bishop on d5 is light-squared, and so the black king can sit on g8 and h8 for the rest of time. Push the pawn to h6 and bring the king to g6 and it is stalemate. The extra piece buys nothing at all, and the engine knows it because it looked ahead rather than counting the pieces.
That is the point to take away. The evaluation is not a sum of material. It is the engine’s opinion about the result, expressed in pawns because pawns are a familiar unit, and modern engines learned most of that opinion from playing rather than from any table of values.
How much of it to believe
Two things go wrong when club players read the bar.
The first is treating small numbers as verdicts. Anything under half a pawn means the game is on. Between a half and one and a half, somebody is slightly better and both sides still have work to do.
The second is forgetting who has to play the moves. An engine’s +2.5 assumes engine play from here. In a game between two humans at forty minutes each it may mean the position is easier to handle, nothing more, and a losing position with counterplay scores worse and wins more often than a passive one.
Where the numbers really earn their keep is after the game. Run the analysis, look at the moves where the score jumped by more than a pawn, and ask what you missed. Those jumps are exactly what the labels inaccuracy, mistake and blunder are measuring, and three of them per game is a normal club score, not a disaster.