After a verb, 上 works as a directional or resultative complement. It marks upward motion or successful attachment / completion: 穿上 (put on clothing), 关上 (close shut), 爱上 (fall in love with). The tone often softens to neutral shang in this complement role.
usage
With time words, 上 means 'previous / last': 上个月 (last month), 上次 (last time), 上周 (last week). Mirrors 下 for 'next' - 下个月 is next month.
register
Dictionaries also list a niche reading shǎng, used only in the linguistics term 上声 (the third tone of Mandarin) and a couple of derived compounds. Outside of tone-name discussions, every 上 you meet is shàng (or its neutral-tone variant shang).
Bottom horizontal is the 一 radical, serving as the reference baseline against which the upward marker is read. It is also the indexing radical for the whole character, which is why dictionaries file 上 under 一.
ideograph
⺊bǔ
upper marker; vertical-plus-tick indicator
The vertical with attached tick is an abstract pointer aimed above the baseline. Together with the base 一 it forms a classic 指事 indicator graph: the mark shows position above the ground line and therefore means up, over, on top.
