In the phrase "look forward to...",  we use to as a proper preposition, and not part of an infinitive ("to verb") form.

"I look forward to meeting you" is correct.  "I look forward to meet you" is incorrect.

If you're not sure if you should use a gerund, then remove the gerund and put another noun there.  Gerunds function as nouns, remember?

"I look forward to tomorrow."

"I look forward to your reply."

"I look forward to summer."

"I look forward to a pay rise."

In all examples, the sentence still makes sense. So in this case, if you use a verb form after to, then it must be a gerund. :)

Hi Ingridy,

Gerund phrases come in a few forms. Example are : 1. Simple subject 2. Predicate Nominative, 3. Direct Object 4. Object of a preposition. 

In your case, the gerund phrases is case 4.

"to meeting you" is a gerund phrase and it also happens to be the object of the proposition "to". 

Thus, the word "to" is not part of the infinitive .

A second way to explain is this:

"Look forward to" means "like"

Therefore, we would write: I like meeting you (correct) and not I like meet you (incorrect). 

This is the best explanation I can provide.

Hope this helps. 

Cheers, Lance