A legume is a type of botanical fruit consisting of a long pod which splits open along two seams and the (typically multiple) seeds inside. The term does not have much of a separate culinary meaning, but it's often used to only refer to beans and peas. The botanical classification also includes other "fruits" such as peanuts, although this may be a bit of a confusing use of the word for the average person.
Many legumes are eaten as vegetables, although legumes do have their own special culinary category of "pulses" for beans, lentils, and certain other legumes that are dried before cooking and eating them.