A minute is a small part: pars minuta, the first small part an hour was cut into. Cut each of those into sixty again and you had the pars minuta secunda, the second small part, and that is the whole of its name. The second is called the second because it came second. There were thirds after it, sixtieths of a second, and a few astronomers used them, but the word never caught on. So the unit the atomic clocks are built to keep is named for its place in a queue that stopped one step after it.