Domain is essentially what values are applicable(valid) for x.

Ex:

In this case the domain is:

(All real numbers)

There is a vertical asymptote at 1.

Range is essentially what values are applicable(valid) for y.

Ex:

In this case the domain is:

(All real numbers)

There is a horizontal asymptote at 1.

For more info:

Domain of a function - Wikipedia, the free encyclopedia

Range (mathematics) - Wikipedia, the free encyclopedia