1520s, originally "a second crop of grass grown on the same land after the first had been harvested," from after + -math, which is from Old English mæð "a mowing, cutting of grass" (from PIE root *me- (4) "to cut down grass or grain").
Other words for it were aftercrop (1560s), aftergrass (1680s), lattermath, fog (n.2). The figurative sense is by 1650s. Compare French regain "aftermath," from re- + Old French gain, gaain "grass which grows in mown meadows," from Frankish or some other Germanic source similar to Old High German weida "grass, pasture."
When the summer fields are mown,
When the birds are fledged and flown,
And the dry leaves strew the path;
With the falling of the snow,
With the cawing of the crow,
Once again the fields we mow
And gather in the aftermath.
[Longfellow, from "Aftermath"]
It forms all or part of: ab-; abaft; ablaut; aft; after; apanthropy; aperitif; aperture; apo-; apocalypse; apocryphal; Apollyon; apology; apoplexy; apostle; apostrophe; apothecary; apotheosis; awk; awkward; ebb; eftsoons; of; off; offal; overt.
It is the hypothetical source of/evidence for its existence is provided by: Sanskrit apa "away from," Avestan apa "away from," Greek apo "from, away from; after; in descent from," Latin ab "away from, from," Gothic af, Old English of "away from."
Alternative etymology (Watkins) traces it to Proto-Germanic *furthera-, from PIE *pr-tero- (source also of Greek proteros "former"), representing the root *per- (1) "forward" + comparative suffix also found in after, other. Senses of "in addition, to a greater extent" are later metaphoric developments.
It replaced or absorbed farrer, ferrer as comparative of far (itself a comparative but no longer felt as one). Farrer itself displaced Old English fierr in this job; farrer survived until 17c., then was reduced to dialect by rival farther. "The primary sense of further, farther is 'more forward, more onward'; but this sense is practically coincident with that of the comparative degree of far, where the latter word refers to real or attributed motion in some particular direction." [OED]
"a person's offspring, descendants collectively," late 14c., posterite, from Old French posterité (14c.), from Latin posteritatem (nominative posteritas) "future, future time; after-generation, offspring;" literally "the condition of coming after," from posterus "coming after, subsequent," from post "after" (see post-). Old English words for this included æftercneoreso, framcynn.