出 is a picture of a foot stepping up and OUT of a cave or enclosure (the lower 凵) — leaving, going out. You can read it as two 'mountains' stacked, but it's really a foot crossing a threshold outward.
出 is the partner of 进 — 'out' to its 'in'. 出去 (go out, with 去), 出来 (come out, with 来), 出口 (exit, 'out-mouth', with 口 — the sign you follow to leave any station or mall), 出国 (go abroad, 'exit country', with 国). 进出 = in and out. 出 also means to produce or emit: 出生 (to be born, 'come out into life', with 生), 出现 (to appear, with 现 — which you learned!). Whenever something comes forth, it's 出.
A foot stepping up and out of an enclosure — to GO OUT.
出口 ('out-mouth') is the EXIT sign in every station and mall — follow it to get out. 出国 = go abroad ('exit the country'). 进/出 = in/out, a pair you'll use daily.