Galangal (also known as galanga, galingale, and anything with a smattering of g's and a's) is a rhizome similar to ginger that is popular in Thai cooking.

It has an oddly floral aroma, compared to the earthy spiciness of ginger. Finding it fresh is possible, but it'll be super expensive. I recommend the frozen version - you can track it down at the Thai grocer on Bayard St (check out the map for the Thai class).

You can also find it dried, which is super cheap but not nearly as pleasant. If you end up using the dried stuff, soak it in warm water to reconstitute it.