Gerunds and infinitives cause problems because the guidelines for using them are not always clear. I use guidelines instead of rules because the best grammarians and linguists seem to be able to do is give some guidelines and lists of words.

A gerund is an -ing form of a verb used as a noun.

Dancing is a lot more fun than studying.
I like swimming more than water skiing.
He is a fool when it comes to dancing.

A gerund is different from a present participle because it functions as a noun while a participle functions as an adjective.

The dancing girl left everyone watching in admiration. (participle)
The girl excels at dancing. (gerund)

Gerunds come at the beginning of a sentence more often than infinitives. They also can be possessed. In other words, a noun or pronoun coming before a gerund should be in the possessive.

I really admired his dancing last night.
John's dancing shows a definite need for lessons or an operation because he seems to have two left feet.