Toward, near, addition
Ad- comes from Latin "ad" (toward, near, in the direction of) and signals movement toward something or addition to something. It is one of the most common prefixes in English: adapt = fit toward a new use; admit = let toward the inside; advance = move toward; attract = pull toward; advise = speak toward (give direction). It generates massive numbers of Latin-based English words.
Twelve forms of ad-
Ad- assimilates to the consonant that follows it, producing up to twelve forms: ac- (accept, access), af- (affect, afford), ag- (aggress, aggravate), al- (allow, allocate), an- (announce, annoy), ap- (appear, apply), ar- (arrive, arrange), as- (assist, associate), at- (attract, attend), and a- (ascend, aspire). The double consonant is the clue: affect = ad+fect, arrive = ad+rive, assist = ad+sist, attract = ad+tract.