Simply put, non-finite verbs are verbs which are NOTfinite verbs. Looks very simple, but it's not entirely so.
The basic points of difference between finites and non-finites are...
A non-finite verb does not change according to its subject, as a finite verb does. He likes to drive. They like to drive. The non-finite verb to drive remains constant, while the finite verb like/likes changes (number and person) according to the subject he/they. You can read more about this point in the subject-verb agreement page.
Non-finite verbs are not affected by tense changes, finite verbs are... They like to drive. They liked to drive. The finite verb shows two different forms like and liked for the simple present and simple past tenses respectively. For the non-finite verb to drive, tense is irrelevant.
Why Are Non-finites Called Verbals?
We often call the different types of non-finite verbs a "verbal something," depending on the non-verblike work they do. So the word verbal becomes a kind of generic (common) name for them. There are three types of Non-finite verbs, the Infinitive, the Gerund, and the Participle.
the Participle is often called a verbal adjective.
The Infinitive too does the work of a noun, or an adjective, or an adverb (adjective modifier, purpose modifier, etc). We usually don't call the infinitive a verbal noun or a verbal adjective, only because we don't want to confuse it with the gerund or the participle.
What do we need to learn about Verbals?
Besides what we have already seen above, we need to learn about their different types.
(Follow the links below for the three different non-finite verbs.)