We shall look at this particular type of verb from three angles:
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.
If we look at the function, that is, the work an infinitive does in a sentence,
we see the following two functions...
Look at this example:
I like to finish the work quickly.
In this sentence, the phrase 'to finish' does the following jobs:
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!
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.
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 meanings as time, factualness, command, possibility, activity, passivity, etc. The infinitive in itself (semantically) is a pure action word - to do, to write, etc) or a word denoting existence - to be.