While "splitting infinitives" sounds like something Superman would do to save Metropolis, our English teachers might've had us believe that it was only fit for villains.
The full infinitive is the "true" form of the verb; that is, the verb without conjugation. To go, to eat, to do, to split an infinitive -- you get the idea. When we talk about splitting infinitives, we mean we stick an adverb in the middle of the full infinitive.
To bravely ask. To boldly go. To tediously list.
Scandalized, aren't you? How dare we ... put those adverbs there.
Exactly. It doesn't sound wrong. But in the 19th century, an English grammar book argued that it wasn't common usage. In addition, you can't split infinitives in Latin since they're one word (currere) rather than two (to run), and Latin was still a big deal back then. Accordingly, people went along with the decree forbidding split infinitives [source: Fogarty]. But it didn't entirely catch on because pesky "common usage" really did win out. We split infinitives, with perfect comprehension, all the time. Now we can choose to keep them together or to split them smugly, knowing we're on the right side of grammar.