1. To eat something with great enjoyment.
2. To mouth and/or bite someone in a sexual or non-sexual way.
3. An exaggeration of the noise made during one or both of the above activities, as originated by Lolcats
"I'm so hungry. Let's get something to nom."
"Oh man... I want to nom him lots."
"And she was all like, 'Om nom nom nom.'"