If a function is even, the graph is symmetrical about the yaxis. If the function is odd, the graph is symmetrical about the origin.

Even function: The mathematical definition of an even function is f(–x) = f(x) for any value of x. The simplest example of this is f(x) = x^{2} because f(x)=f(x) for all x. For example, f(3) = 9, and f(–3) = 9. Basically, the opposite input yields the same output.
Visually speaking, the graph is a mirror image about the yaxis, as shown here. 
Odd function: The definition of an odd function is f(–x) = –f(x) for any value of x. The opposite input gives the opposite output. These graphs have 180degree symmetry about the origin. If you turn the graph upside down, it looks the same.
The example shown above, f(x) = x^{3}, is an odd function because f(x)=f(x) for all x. For example, f(3) = 27 and f(–3) = –27.