Finite verbs are those that occur in various tenses, moods and aspects, and that can change in the sentence depending on the subject. Here are some examples:
He is sitting.
I will have been rushed.
Nonfinite verbs are of three kinds only-- '-ed' and '-ing' forms standing alone, and infinitives. Here are some examples:
The man standing in the corner is my husband.
Painted by daVinci, the Mona Lisa hangs in the Louvre.
I like to sit in the sunshine.
Let me help you with your coat.