Finite Verbs vs. Non-Finite Verbs

Finite verb forms are namely, conjugated verbs that show person, number, tense, aspect, and voice. Finite verbs, as opposed to non-finite verbs, can function as the main verb of an independent clause. Non-finite verb forms, or verbals (infinitive, past participle, present participle, and gerunds by themselves) are not limited by the subject and serve as other parts of speech in the sentence (nouns, adjectives).
The children were talking to each other when the teacher came in.
[the present participle talking is part of the finite verb were talking, the main verb of the independent clause The children were talking]

The talking children made the teacher angry.
[the present participle talking is a non-finite verbal modifying the noun children and cannot be the main verb of this independent clause]

Talking is the children’s favorite pastime.
[talking is here a gerund, a verbal noun functioning as the subject of the independent clause]