给 = 纟(silk thread) + 合 (to join). Its old sense was 'to supply / provide' (handing over goods, even bolts of silk). From supplying came the everyday meaning: to GIVE.
给 (gěi) is 'to give', and also marks the receiver, like English 'to/for': 给我 (give me / for me), 给你 (for you), 我给他书 (I give him a book). It's one of the most useful verbs for daily life — handing things over, doing things for people: 给我看看 (show me, 'give me a look'). Note: 给 can also read jǐ in formal words like 供给 (supply), but in speech it's gěi.
Handing over a thread (纟) joined (合) to another's hand — to GIVE.
给 marks who receives, like English 'to/for': 给我 (for me), 给你打电话 (call you, 'give you a phone call'). It turns almost any action into 'doing it for someone'.