In its simplest form, and eye patch is nothing more than a slightly oval shaped piece of cloth that covers a damaged or lost eye.
Symbolically, an eye patch is usually used to indicate extra knowledge or wisdom on behalf of the character. One ancient example is Odin, the Norse God who sacrificed one of his eyes for wisdom. For a more modern example, look at the character of Solid Snake in Metal Gear Solid 4; while it isn't a normal eye patch, it still gives Snake an advantage of extra knowledge that others do not have. Vyse of Skies of Arcadia has a similar faux eye patch that allows him to examine his surroundings with technological aid.
Another symbolic use of the eye patch is to designate someone who is at the least a rebel, and at most an outlaw. This is seen most often in the portrayal of pirates as having only one eye. This is most likely due to the natural inclination to view people who are different with some suspicion. This trait has also been the subject of parody, as a character with two fully functional eyes may wear an eye patch for the supposed intimidation factor it brings despite the loss of depth perception suffered by wearing it.