A noodle is a piece of pasta, especially a long, skinny one. You can eat noodles with butter and cheese or sauce, or slurp them from a bowl of soup.
Noodles are cut or rolled from a dough that contains some kind of flour — wheat, buckwheat, and rice flour are all commonly used. In Thai food, you'll find wide and thin rice noodles, while Italian food contains many varieties of noodles made from semolina flour, like spaghetti and lasagna. Informally, you can call your head a noodle too. Both meanings have uncertain origins; all we know for sure is that noodle comes from the German Nudel.