What is the purpose of a title sequence

There are many purposes when it comes to the point of a title sequence.
For example:
Crediting - Actors and people who created the film can be credited for the work they've done, from this they can make a name for themselves. Also production companies are credited in the films titles the advertises the company , this also begins to establish expectations from audiences.
To set - From a title sequence theme or genre can be set up giving the audience some understanding what the films going to be like. For example if the film has someone in the title sequence selling drugs it gives the impression that the film genre is crime.

In general film sequences are there to make the viewer want to go on , as they would be intrigued thinking what the film is going to be about. Most good films have a good opening sequences what match up to the expectation of the film. It can be good to show something memorable in the opening for the viewer to remember throughout the film.