The infinity symbol looks like a sideways 8.  In mathematics, the infinity symbol represents the concept of a number that goes on and on indefinitely, like pi (3.14159265359…).  When used to describe feelings, or space, or any other concept, it means limitless and boundless.

The infinity symbol has become popular recently as a jewelry trend.  Being given a piece of jewelry with the infinity symbol means forever and always, never-ending possibilities, eternity.