1. Pleasing to the sense of taste. Scrumptious. Delicious.
2. Cute, fabulous. What a totally yummy dress! While definition 1. is found in most dictionaries, this sense of yummy is still well into the realm of slang.
3. Acronym (kind of) for Young Upwardly Mobile MommY. A pun on Yuppie, basically meaning a working mom.
Etymology: from the word yum, which in turn is said to derive from the sound of smacking lips.
Also spelled Yummi. (This is not a spelling recognized by any dictionary I've found -- it's a word in the same sense that Kwik and EZ are. But with 712,000 matches on Google, I'll count it as a 'common law' word.)