A finite verb (sometimes called main verbs) is a verb that has a subject, this means that it can be the main verb in a sentence. It shows tense (past / present etc) or number (singular / plural).
I live in Germay. (I is the subject - live describes what the subject does - live is a finite verb).
A non-finite verb has no subject, tense or number. The only non-finite verb forms are the infinitive (indicated by to), the gerund or the participle.
I travelled to Germany to improve my German. (To improve is in the infinitive form).