It does mean "jumped", but you would always need a subject with it to express that meaning. "Léim mé": I jumped. The past tense (and not only) of the verb to jump just happens to end in -im. It's not a personal ending.
"Léim" on it its own could only mean "I read"; here, there is no extra subject pronoun, so it's clear that the -im means "mé"
(And indeed, you can say léann mé = "I read")