A non- finite verb is a form of a verb that does not have a subject and and does not exhibit tense and number in an independent clause or sentence. In English, the non-finite verb forms are infinitives and gerunds and participles. Non-finite verbs are distinguished from finite verbs which show a distinction in tense and number, and may stand alone as the main verb in an independent clause.
They are writing the letter. - They is a subject; are is a finite; writing is a non-finite verb (which does not exhibit tense nor number); the match is an object.
Verbs that do not change with change in number and person of the subject, are known as non-finite verbs. These verbs perform the function other than that of a verb. They may work as nouns, adjectives or adverbs.
Non-finite verbs are broadly classified into three main types, i.e. Infinitives, Gerunds and Participles.