I.e. is the abbreviation for the Latin phrase for 'id est', which means 'that is'. It is used when you are clarifying something, especially when you are restating something. It is often defined, in English, as meaning 'in other words'.
"Ted is a special case... i.e., he's an idiot."
Style guides give different specifications on usage, but unless otherwise required by your professional or academic setting, i.e. will usually be followed immediately by a comma. I.e. is most often used in parenthetical remarks (i.e., like this), but when this is not the case one usually uses a pair of adverbal commas, i.e., like this.
It is sometimes confused with e.g., which is used when you are giving an example by listing some, but not all, members of a set.