Disdainful means scornful and arrogant. To be disdainful is to act mean and superior.
If you're acting haughty, imperious, lordly, overbearing, prideful, sniffy, supercilious, or swaggering, you're acting disdainful. The great Michael Jordan was known to be disdainful of his opponents — and even teammates who couldn't keep up with him. Arrogant people with their nose in the air are disdainful. This can also have an even harsher sense, meaning contemptuous. Either way, that person who gave you the disdainful look doesn’t like you (or at least something you did) very much.