Cambridge explains it plainly:
Look forward to something means to be pleased or excited that it is
going to happen. The ‘to’ in look forward to is a preposition, so we
must follow it by a noun phrase or a verb in the -ing form:
- We’re looking forward to going to Switzerland next month.
- I’m looking forward to the holidays.
If the second verb has a different subject, we use the object form of
the pronoun, not the subject form:
- We’re looking forward to him arriving next week. (Not: We’re looking forward to he arriving next week)
We also use look forward to at the end of formal letters and formal
emails to say that we hope to hear from someone or expect that
something will happen. We use the present simple form:
- I look forward to your reply.
- I look forward to hearing from you soon.
"Look forward to" has a pattern: I look forward to [a thing you would like to happen]:
- I look forward to [hearing] from you. "Hearing" is an action [thing] I would like to happen.
- I look forward to [hear] from you. "Hear" is not a thing.
There is a slight difference between:
- I am looking forward to...
- I look forward to...
As for the question whether to use “I look forward to” or “I am
looking forward to”, some people consider the two completely
interchangeable, but most find the phrase with “look forward to”
somewhat formal and best suited for formal correspondence, whereas “to
be looking forward to” is more informal and friendly.
"To" is a preposition in this construction, and since it is a preposition, it should be followed by an object. The object of a preposition can be either a noun, a pronoun, or a gerund (VERB+ing functioning as a noun).
If you use verb without "ing" than "to" is an infinitive:
- I look forward to [to hear] from you. That is absolutely incorrect!
There are more verbs that cannot be followed by an infinitive:
- anticipating, imagining, foreseeing, regretting...