A boot is the kind of shoe that can rise as high as your knee, like riding boots, or just up to your ankle, like silver-studded Beatle boots. To boot means to kick something (with or without the fancy footwear).
Like most fashionable things, the word boot comes from the Old French bote. It used to refer only to riding boots, but now any big ol’ high-rise shoe kind of thing is a boot. Since boots are for feet, when you boot someone, you kick them. If you give someone the boot, you’re kicking him out. A totally different type of booting involves starting up an operating system on a computer.