Most critics are there to give a recommendation to their readers/viewers as to whether it is worth investing their time and money into going to see a particular film.
Their bread and butter is new releases, but a lot also like to talk about older films to bring them to the attention of modern viewers.
They have influence only in the sense that the best ones have (as well as critics collectively as a group such as the case of Rotten Tomatoes and Metacritic) have become trusted by audiences due to their good track records. They don't really influence whether people like a particular movie. But they can influence whether people bother with a movie at all.