Motte is a piece of detached land. Aigue describes something that terminates in a point or has been cut away.
NOTE: that explanation is incorrect. Motte means a mound; aigues is from the Occitan aigas, meaning waters (derived from Latin aquae), as seen in place names like Aigues-mortes and Aigues-vives in the neighbouring prefecture of Gard. Thus La Motte-d'Aigues means the Mound OF Waters, as evinced by its proximity to the Etang (lake) de la Bonde and the River Eze.