We shall look at this particular type of verb from three angles:
how it looks (its form or morphology);
what work it does in a sentence (its function or syntax); and
its meaning (or semantics).
How Can You Recognize an Infinitive?
We can recognize it from its form, which is usually as follows: to eat, to drink, to play, to be, etc. (with a 'to' before it).
In some cases the word 'to' is dropped. We speak of such a verb (with the word 'to' dropped) as a bare infinitive.
The bare infinitive is the standard form of an English verb.
What Work Does an Infinitive Do?
If we look at the function, that is, the work it does in a sentence, we may consider it to be both a noun and a verb.
The Infinitive As Noun and Verb
Here is an example:
I like to finish the work quickly.
In this sentence the phrase to finish does the following jobs:
It is the object of the finite verblike - therefore to finish is similar to a noun (because being an object is a noun's job).
The phrase to finishhas its own object, work - so to finish is a verb (since verbs have objects).
The adverbquicklymodifies (i.e. tells us something more about) to finish. Since the phrase to finish is modifiable by an adverb, it must be a verb.
We can say that the infinitive, though born in the verb family, does not limit itself to being a verb. It often behaves like a noun when it goes around socializing in the world of sentences!
The Infinitive As Adjective or Adverb
In some cases...
It behaves even like an adjective, as in the following sentence.
That was a game to watch!
In this sentence, to watch tells us something more about the quality of the game (a noun). Describing a noun is the work of an adjective.
Sometimes it behaves like an adverb. The sentence below illustrates this.
Her voice is pleasant to hear.
The phrase to hear tells us something more about the quality of being pleasant. The word pleasant is an adjective, and words that tell us more about an adjective (adjective modifiers) are traditionally called adverbs.
The Infinitive and Meaning.
If we take the meaning (semantics), then the infinitive could be viewed as a pure, unadulterated form of a verb.
This pure meaning we modify, change, or mutate, by imposing on it such things as tense, modality, voice, etc. The infinitive in itself (semantically) is a pure action word (to do, to write, etc) or a word denoting existence (to be).
For further reading...
Now that you know about the Infinitive, you may want to learn about the other two non-finite verbs: the gerund and the participle...