If you let someone do something, you decide that they can do that thing if they want to. If you don't let someone do something, you decide that they can't do that thing.
It is an irregular lexical verb which is uninflected for its preterite and past participle (i.e. all are "let" /let/). It has a third person form "lets" (/lets/), and an -ing form "letting" (i.e. with a double T). It catenates with a bare infinitive rather than a to-infinitive, similarly to its antonym make.
The Imperative form "let's" has special properties and its own Teflpedia article.
Note that "let me" can be reduced to /lemi:/ which can be written "lemme"
Learners may try to use a to-infinitive in place of the bare infinitive e.g. *"I let it to go". Let and make are often confused by Chinese speakers as both correspond to the Chinese verb 让 (trad: 讓, Pinyin: ràng).