Aioli \ahy-OH-lee\ , noun;
1. A sauce made of oil and eggs, usually flavored with garlic, from the Provence region of France
I watch a lot of Food Network. A lot. So I immediately recognized this word*, though I don't think I've ever had it before. Basically, it's flavored mayonnaise. If you've never done it before, I recommend breaking out the food processor and making your own mayo (or aioli). It's really much better than the store bought stuff.
The word is first attested in English in 1914 and is borrowed from French aïoli, which dates to the mid-1700's. It is a combination of ai + oli, which is the old version of ail ("garlic") and huile ("oil").
*It is Dictionary.com's word of the day today