Pictogram (象形) – hand and fingers. The top stroke is the bent over middle finger, while the horizontal strokes are each two fingers. Compare 爪, 寸, 九, 又, and 彐 as a stylized hand.
Note that unlike the other hand/claw characters, 手 has consistently had five fingers: a mammalian/human hand, as opposed to the three digits often found in the others.
Compare also 止 (“foot”), derived from a footprint, originally composed of 3 toes and a sole.
Etymology
STEDT compares this word to Proto-Sino-Tibetan*g-(t)sjəw-k/ŋ(“wing; hand”) based on Karlgren's Archaic Chinese (Old Chinese) reconstruction *śi̯ôg, connecting it to Tibetanགཤོག(gshog, “wing”).
杻 (“handcuffs”) can be written as 杽, so 丑 (OC *ᵇhnruʔ) (with a nasal initial) and 手 seem to be interchangeable as phonetics.
The ancient graph 丑 resembles the graph of 又 (“right hand”). 狃 (OC *ᵇnruʔ, “animal track; claw”) seems to be the modern specialized form of 丑, which has been borrowed to represent an earthly branch.
As done by Sagart (1999), Baxter and Sagart (2014) put 杻 (OC *n̥<r>uʔ, “handcuffs”) and 狃 (OC *Cə.n<r>uʔ, “animal track; claw”) into the same word family as 手 (OC *n̥uʔ). Zhengzhang (1995) suggests a connection to Burmeseညှိုး(hnyui:, “forefinger”), which STEDT derives from Proto-Sino-Tibetan*s-njuŋ ~ *s-m-juŋ ~ *s-m-juw(“finger”).
Alternatively, Schuessler (2007) suggests a tone B endoactive derivation from 收 (OC *nhiu?, “to take; to gather”), literally “that which is doing the taking”.