You can see yourself in a mirror because light rays bounce off its shiny surface. Light rays come from everything you can see, including yourself. You see things when the light rays from them enter yours eyes. Some of the light rays that come from yourself strike the mirror. The mirror reflects the rays because it is very smooth. The rays come back to your and enter your eyes.
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The light rays, that come from things move in straight lines. However, when they are reflected from a mirror, the light rays change direction but still travel in straight lines. As light rays are invisible, you cannot see that the rays from yourself have been reflected by the mirror. Your brain is tricked into thinking that the rays have come direct to you in one straight line without being reflected, as if as copy of yourself were standing on the other side of the mirror. You, therefore, see an image of yourself (the left side, say) back to you on the left. In the mirror, your left side appears to be on the left. But when real people face you, their left side is always to your right.