The best, shortest, and most easlily understood definition goes as fallows:

An infinitive is the form of a verb that comes after to, as in to support or to write; it’s the uninflected form of the verb. A split infinitive occurs when another word comes between the to and the verb. Some people prefer to keep the to next to the verb at all times, and though grammar experts are divided over this rule, it’s probably better to avoid split infinitives whenever possible. Instead of “Matt seems to always do it that way,” try “Matt always seems to do it that way.”

Enjoy you grammatical nuances……