To quote Felicia:
"It's a japanese word that translates into "Bonus" or "Extra"."
You may find omakes on anime DVDs included as extras, or simply as extras in any other sense of the word.
They usually include a total change in style as well as a humoristic view. Making fun of the previous stories and such.
Did you watch the latest Soul Taker omake?
The KGNE omakes were 1337!
This term has become popular on many fanart or anime sites. It is also used on various other web sites. It's a japanese word that translates into "Bonus" or "Extra". It basically involves any material on the site that does not fit into any of the other site's catagories. Such as downloads, photos, rants, or links.
"Did you check out the omake area of my site?"