not a finite form, that is, not indicating person or tense
In many languages the distinction is a lot clearer than in post-1066 English. In Esperanto, all infinitives end in -i, and no finite forms do
It is essentially the basic form of a verb and the one under which it is listed in the dictionary, e.g. 'to have', 'to be', etc. Not all languages have an infinitive. They are a form of non-finite verb, i.e. verbs that cannot perform an action in an independent clause. Infinitives can also be used in sentences as nouns, adjectives and adverbs.
A verb with 'to' in front of it.
To eat, to work, to run, to sleep etc.
The exact definition depends on the specific language in questions.
English has two forms of the infinitive:
1. the bare infinitive - the dictionary form. be, have, go, do, see, listen, etc. It's used with modal helping verbs (can go, may have, should be, might see, must listen, etc).
2. the full infinitive -- TO is included: to be, to have, etc. In English specifically, it can be used as a noun, adverb, or adjective (not true of all languages that have an infinitive).
There are languages without an infinitive form.
Note that most forms of the simple present tense in English happen to look the same as the bare infinitive. I see, I have, they listen etc (but not: I am, they are, etc), but they are not infinitive forms despite looking identical. In many other languages, the infinitive does not look the form of any tense.
參考: studied linguistics and English grammar; native English speaker