An ELT Glossary : Finite and non-finite verbs
A finite verb is a form of a verb marked for tense, person and/or number, and used in a sentence to show that it is related to a subject. Eg :
John has worked in Lancaster since he left school, although he lives in Manchester.
has worked : marked for present tense, 3rd person, singular by the "s" in has
left : marked for past tense by the irregular past tense form
lives : marked for present tense, 3rd person, singular by the "s"
A non- finite verb is a a form of a verb not marked for tense, person and/or number, and not directly related to a subject in the same clause. The base form used for the imperative or infinitive and the participle forms of the verb are non-finite forms. Eg :
a) He's not the right person to ask about that.
b) Located on the coast, the hotel has fine views of the sea.
c) Rushing to catch the bus, I tripped and fell.
Notice that there is no information about who/what the subject is in the clause itself - it has to be retrieved from the main clause in the rest of the sentence. Nor is there any information about tense (despite the misleading names of "present" and "past" participle). It is only by looking at the verb in the main clause that we can infer whether the event is past, present or whatever.