What is an infinitive and what is a split infinitive?

An infinitive is the basic form of any verb - in English, it takes the form of the word TO + the verb itself. For example: to play, to dance, to read, to sleep, etc.

On the other hand, a split infinitive is a type of an infinitive where the word TO and the verb itself are split, because there is some word inserted between them. For example: to really like something, to boldly go, to gradually do something, etc.

An infinitive is the basic form of a verb, without an inflection binding it to a particular subject or tense and a split infinitive is a construction consisting of an infinitive with an adverb or other word inserted between to and the verb.