To halve something is to divide it into two equal parts. When you share a pizza with your best friend, you can cut it in half, or halve it.
A recipe might instruct you to halve an onion, and a little kid might request that you halve her peanut butter sandwich and cut the crusts off. You can also halve less physical things — you can halve your expenses if you reduce them by half, or halve the bill for lunch with your sister, if you split it with her. Halve comes from half, originally an Old English word meaning "side" or "part."