I found this question in an online test.
We're really looking forward to going on holiday. (Right answer)
We're really looking forward to go on holiday. (Wrong answer)
I do not understand why the first one is the right answer.
'going' is a gerund - a verb used as a noun. 'going' is the object of the verb 'looking forward to'. We would never use the second method. Using a verb ('looking forward') followed by an infinitive indicates the missing words 'in order'. For example " For example 'I go to the gym to get fit'. Perhaps used in conversation and not in formal text.