A split infinitive occurs when to is separated from the infinitive by an adverb or adverbial phrase. It used to be considered the cardinal sin of good English, but it’s now accepted that there are many instances when a split infinitive is justified. In general, however, it is easy enough to avoid.
(i) She did not want to entirely surrender to his will.
(ii) He was instructed to discreetly talk to the Press.
In both sentences there is no need for the split infinitive, as the adverb (entirely, discreetly) can be placed outside the infinitive like this:
(i) She did not want to surrender entirely to his will.
(ii) He was instructed to talk to the Press discreetly. or,
(iii) He was instructed to talk discreetly to the Press.
The easiest rule to remember about the split infinitive is to avoid it, as long as there is no doubt that the meaning will be ambiguous or awkwardly expressed as a result.
I can hear you all mumbling into your coffee; “Yes, I know, but what is the woman talking about?”