e.g. stands for exempli gratia. It's Latin. That probably doesn't mean much to most of us.
Or for our purposes, let's just say e.g. means "for example," or "such as."
Used in a sentence: I'm a big fan of mainstream, flannel-shirt-wearing, 90s rockers (e.g., Stone Temple Pilots or Pearl Jam).
i.e. is Latin for id est.
Simply put, i.e. means "in other words" or "put another way."
Used in a sentence. I'm a big fan of mainstream, flannel-shirt-tastic, 90s rock music (i.e. "grunge rock").
A colleague of mine says he remembers the difference between "e.g." and "i.e." by thinking "e.g." stands for "example given."
Go forth and impress people with your ability to use e.g. and i.e. appropriately — they're misused way too often.