Strictly speaking, itadakimasu is the polite form of the verb itadaku, which now means "to receive" but is derived from the noun itadaki, which now means "summit" (e.g. of a mountain), and used to mean "top."

How did this happen, you ask?

Well, in Japan, you eat out of a little rice bowl that sits in your hands. A long time ago, people used to raise their rice bowls to the host when receiving food, kind of like a toast... as a way of signifying that the host's food was "above them." When they did this, they would accompany it with the typical Japanese gesture of explaining what they were doing: "I lift my bowl!"

Even when people stopped lifting their bowls, they continued to say itadakimasu, and the practice continues today.

Incidentally, you can also use itadakimasu to request things. I've become fond of saying:
Kôhî o itadakemasu ka?
Can I get some coffee?
Note that because itadakimasu is humble keigo, you can only use it when referring to yourself. You're the one doing the receiving. If you're talking about someone else, you have to use honorific verbs such as meshiagaru.