Symmetry means that if you draw a line through something, usually down the middle, then the two halves of it are identical but reversed - like looking into a mirror. Things that are symmetrical are usually nice to look at.
People's faces are symmetrical because if you draw a line down the middle of your face the left and right sides are the same. In fact, your entire body is symmetrical, as are animal's faces and bodies. Lots of everyday things are symmetrical. How many symmetrical things can you see around you?
The picture is a shape that is symmetrical along the left and right half and the top and bottom halves.
The opposite of symmetry is asymmetry.