Tears are made up many substances secreted from various parts of the lacrimal system. The conditions collectively referred to as "dry eye" can occur for many reasons, the most obvious reason being insufficient quantity of tears. An aqueous deficiency refers specifically to inadequate production by the lacrimal glands of the watery part of the tears.
Aqueous deficiency is what really properly ought to be called "dry eye" - when you're aqueous deficient, you really are dry. This is contrasted with meibomian gland dysfunction, where the primary problem is - or at least starts out as - poor production or secretion of the oil layer. However, the lines become blurred as the diseases progress.
Aqueous deficiency is most frequently associated with auto-immune diseases (most notably Sjögrens Syndrome). Other well known causes are LASIK or other laser eye surgeries, where patients experience primary aqueous deficiency at least temporarily, and some permanently, due to severing of the nerves; and side effects of many medical treatments such a radiation or chemotherapy which may cause permanent damage to the lacrimal glands.