To graduate means to successfully complete your schooling, to become "a graduate." When you graduate from high school, you become a high school graduate and congratulations are in order.
A graduate is someone who has received a degree from a school. As a verb graduate refers to the act of receiving this degree “I plan to graduate from college in the spring,” or the act of giving a degree “I want to graduate all of my students.” In a scientific sense, graduate can mean to calibrate for fine adjustments. To make a thermometer, you have to graduate it by degrees so it displays a range of temperatures.