Originally a pictograph of a belt or sash tied around the waist — something you carry on your body. The sense extended from "wear/carry on one's person" to "bring along" more generally. The traditional form 帶 still clearly shows the belt motif at the top.

带 is extremely versatile in daily Mandarin. Beyond "bring/take," it commonly appears in compounds: 带孩子 (dài háizi, "look after children"), 带路 (dài lù, "lead the way"), and 领带 (lǐngdài, "necktie" — literally "collar-belt"). It also means "to contain/include" in phrases like 这个菜带点辣 ("this dish has a bit of spice"). Don't confuse it with 戴 (dài), a near-homophone that specifically means "to wear" accessories (glasses, hats, jewellery).