Hâi (ให้) has a few different uses — understand them by ear here. It starts out as "give", and everything else here is that idea stretched: buying something for someone, doing one thing so that another can happen, letting or making someone do it, telling them to, and — as ทำให้ — causing something to happen: ฝนตกหนักทำให้น้ำท่วม, "the heavy rain flooded the road".