What is the definition of symmetry?

Hi there,
can someone give me a (detailed, if possible) definition of symmetry? I'm just confused, because 6 chairs in a line has a symmetrical shape as well. So I think symmetry has a different meaning here.
Thanks! 
First of all, I want to apologize for being so late, and also let you know I'm new at this, so I'm probably wrong. But I'll try my best to explain. I think he means that you can rotate the hexagon and shift the positions of A and B, but it won't matter because this shape is closed. But if you looked at a line of chairs, and for example, A sat on 1 end and B sat on the other, they wouldn't be sitting next to each other, well, because its a line. Again, I don't have any experience teaching math compared to Po shen loh, but I hope this helped!
pinkunicorn4000