In statements like "*it's letting up*" the word "it" functions as a dummy subject called an [expletive][1] (defined as *a syllable, word, or phrase inserted to fill a vacancy (as in a sentence or a metrical line) without adding to the sense*).

In your example of "*it's letting up*", "it" refers to adverse weather conditions, usually rain. You could say "*the rain is letting up*". Like other pronouns, "it" doesn't have to be something previously mentioned if it is really obvious what you are referring to, such as a person looking up at the rain and assessing it.

However, "it" does not always need to refer to any specific noun or pronoun. An expletive serves a grammatical purpose to fulfil the requirement for a subject in English sentences, particularly when talking about things like the weather, time (eg "*it's late*"), distances (eg "*it's a long way*"), and other situations.


  [1]: https://www.merriam-webster.com/dictionary/expletive