When something is divided into two equal sections, half is one of the two parts. You can split a brownie in half if you want to share it with your friend.
You might live half the year in Alaska and half in Florida — in this case, you spend six months, one half of a 12-month period, in each state. You can also divide food in half or save half your paycheck each week, while spending the other half. Your half brother is a sibling who shares one of your parents; you and he might have the same mother but different fathers. In Old English, half means "side" or "part."