Internet, hence the lower case 'e', like in email.
Someone who has a cute MySpace/Xanga/whatever picture, that you have never met, and only know over the Internet.
When used towards someone you know in REAL life, NOT the Internet, it means they ae emo cute.
Amy: Aww! Look at what this person said on the forums!
Sam: *reads* That's so sweet!
Amy: I know! It's totally eCute!
Josh: Look at this chick's picture on MySpace! She's hott!
Pete: Do you know her?
Pete: then she's eCute.
Amber: I'm so plain!
Bea: No you're not!!! You're eCute!