A computer program for evaluating chess positions is called an "engine", and you'll find the engine display under the board. There are three continuations (its best three options for the player) calculated by the engine, an overview of the material balance, the evaluation over time and information about the engine in use.
So what do the number 1.02, 1.08, 1.10 mean? The computer assesses the position roughly in units of pawns. Positive numbers mean White is better, while negative numbers show an advantage for Black. In this example White is better.
The evaluation over time shows how the evaluation changed during the course of the game. You can see that White was soon better and then his advantage grew.
The material balance (who has more pawns or pieces) is even in this example.