Question

What is an infinitive and what is a split infinitive?

Answer 1

Infinitive is the basic form of a verb. It consists of a verb TO and the verb itself. For example: to read, to sleep, to dance, to play, to imagine, etc.
On the other hand, a split infinitive is when you introduce a word between TO and the verb, and thus interrupt the natural flow of the infinitive. 
For example: to really like something, to boldly do something, etc. 

Answer 2

An infinitive is a verb in its basic form that sometimes functions as a noun and is usually preceded by to in English. For example, to run, to think, to imagine, etc. A split infinitive occurs when a word, usually an adverb, is placed between the verb and to (for example, to quickly run, to barely imagine, to freely think). (PLATO)