When you educe you first see the potential in something and then develop it. An artist sketching on scratch paper might later educe a painting from the casual sketches.
Educe can also be used as a synonym for deduce, meaning "to reach a conclusion." Suppose members of a jury have to decide whether someone is guilty of stealing. They use the facts in the case to educe the thief's motivation. Educe comes from the Latin word ducere, meaning "lead." Think of educe as leading to something else.