A transitive verb is a verb that can take a direct object. In other words, the action of a transitive verb is done to someone or something. Most verbs are transitive.
A transitive verb contrasts with an intransitive verb, which is a verb that does not take a direct object. In other words, it is not done to someone or something. It only involves the subject.
In the examples below, the transitive verb is italicized and the direct object (i.e., the thing being acted upon) is in bold.
Lee eats pies.
(Eats is transitive because you can eat something.)
Lee loves mince pies.
(Loves is transitive because you can love something. Note that direct objects aren't usually single words. They're usually noun phrases, i.e., more than one word.)
Lee bought dozens of cakes.
(Bought is transitive because you can buy something.)