Learn more about Grammar:
Adjectives: An Easy Guide with ExamplesAdverbial Clauses: What Are They?AdverbsAnalogy: Definition & Meaning (with Examples)ArticlesBad AdverbsClauses: Definition, Meaning, and How to Use ThemConjunctionsCoordinating Conjunctions: What Are They and When Should You Use Them?Dangling ModifiersDeclarative Sentence: Examples + MeaningExaggerationHomophones: Definition and ExamplesHow to Use Subordinating ConjunctionsInfinitivesInterjections: Definition, Meaning, and ExamplesIntransitive Verb: Definition, Meaning, and ExamplesNounsParticiples PluralsPrepositional Phrase: What Is It & How to UsePrepositionsSplit Infinitive: The Complete Guide (with Examples)Subordinate Clause: Definition, Types, and ExamplesThe Complete Guide to Transitive VerbsTransitions: A Complete Guide (with 100+ Examples)Types of VerbsVerbsWhat is a Pronoun? Rules and ExamplesWhat Is Symbolism in Writing?Word ClassesWhat is a split infinitive? And when should you avoid using one?

Infinitives are two-word forms of verbs, such as to run, to research, or to suggest. A split infinitive happens when you insert an adverb in between to and its verb in an infinitive phrase. Consider the following:
to quickly run
to diligently research
to calmly suggest
The traditional grammatical rule is to avoid this split, putting the adverb after the infinitive:
to run quickly
to research diligently
to suggest calmly
This way, you know what the action is (run) before you know the manner in which it is happening (quickly).
But there are always exceptions to the rule. Sometimes a split infinitive works better than an infinitive. The most famous example is:
to boldly go where no man has gone before
If Star Trek hadn't split the infinitive, and had just used "to go boldly where no man has gone before," it wouldn't be the catchphrase it is today.