When you disprove something, you argue against it or give evidence that it's not true. A student falsely accused of cheating on a test will work hard to disprove it.
Even though it took years to be acknowledged, Galileo's theory that the planets revolve around the sun managed eventually to disprove previous ideas that the Earth was at the center of the universe. If your friends think your family is ridiculously wealthy, you can disprove this idea by showing them the tiny house you live in and the beat up old car your dad drives. The Old French source of disprove is desprover, "refute or contradict."