Here "to" isn't a particle of an infinitive verb, but rather a preposition. The only form of a verb that can be the object of a preposition is the gerund (-ing form.)

Hi John, Jonathan is exactly correct. The -ing form a verb used as a noun is called a gerund. All prepositions must have direct objects and all direct objects are nouns, so the noun form of the verb "explain" is required.

JQ and JK have already answered your question. I just want to add that “to explain” is also good. How do you decide which one to use? They end up meaning the same thing but they feel different. The infinitive feels more factual, more straightforward. The present participle feels more descriptive of a process.