Split Infinitives happen when you put an adverb between to and a verb, for example:
She used to secretly admire him.
You have to really watch him.
Some people believe that split infinitives are grammatically incorrect and should be avoided at all costs. They would rewrite these sentences as:
She used secretly to admire him.
You really have to watch him.
But there’s no real justification for their objection, which is based on comparisons with the structure of Latin. People have been splitting infinitives for centuries, especially in spoken English, and avoiding a split infinitive can sound clumsy. It can also change the emphasis of what’s being said. The sentence:
You really have to watch him. (ie. ‘It’s important that you watch him’)
doesn’t have quite the same meaning as:
You have to really watch him. (ie. ‘You have to watch him very closely’)
The ‘rule’ against splitting infinitives isn’t followed as strictly today as it used to be. Nevertheless, some people do object very strongly to them. As a result, it’s safest to avoid split infinitives in formal writing, unless the alternative wording seems very clumsy or would alter the meaning of your sentence.