Symmetry is also the idea that the laws of physics apply to all observers identically, i.e. that regardless of your acceleration, velocity, or position in space and time the same laws of physics apply. You might recognize that symmetry with respect to velocity is sometimes called special relativity, and that symmetry with respect to acceleration is sometimes called general relativity. This is a pretty important concept, since it would make physics a LOT harder if you had to find different laws of physics for different observers. The laws of physics are also symmetric with respect to orientation, that is, it doesn't matter from what angle you are observing something, the same laws apply. There are also symmetries with respect to forces that are called gauge symmetries that are a lot more abstract, and which I only vaguely understand, so I'm not going to try and explain them. There is at least one more kind of symmetry that I really don't understand, which has to do with the spin of the elementary particles. Basically, there are a lot more kinds of symmetry than you might expect, and a lot of them have nothing to do with what something looks like if you look at it in a mirror.