The infinitive is the part of a verb with 'to' in front of it, such as:
It was introduced by 19th-century grammarians to mimic Latin, in which the infinitive is always one word and so cannot be split.
She decided to immediately go to her university.
In this sentence the infinitive 'to go' is divided by immediately, if you read this aloud it sounds awkward. The sentence is greatly improved by rewriting as:
She decided to go to her university immediately.
Split infinitives are popular in modern spoken English. You can justify their use if the meaning is correct and the sentence sounds natural.