Can some1 explain to me what these means and how i can tell if a relation is symmetric or anti or both?

Im reading the definition over and over for like 10x already and i jsut don't understand.

The example they gave in the book is...

set A {1 2 3 4 }

R = { (2,1), (3,1), (3,2), (4,1), (4,2), (4,3) } is antisymmetric...But why??

What is (a,b) and (b,a) and a=b? i dont understand?