It refers to sections of the man pages. They are organized like this:

1. General Commands

2. System Calls

3. Subroutines

4. Special Files

5. File Formats

6. Games

7. Macros and Conventions

8. Maintenence Commands

You got a lot of good answers here, but just so you know: you really only have to remember that open(2) is a syscall and fopen(3) is a library call. That's the important distinction.

The Unix manual is divided into sections (http://en.wikipedia.org/wiki/Man_page#Manual_sections). Section 2 is for system calls. Specifying the section number allows you to disambiguate which section of the manual you want to look in if a man page exists in multiple sections (e.g., "man 1 write" vs. "man 2 write").

It is where it lives in man. man write returns write(1) an application that sends a message to another user. man 2 write returns write(2) the system call mentioned above(or at least it does on Ubuntu).

It's the "man" section. According to "man man", 2 is the section for system calls. Often you'll have manpages for the same name under different sections, for example sync(1) is a command while sync(2) a system call (which, unsurprisingly, the sync command uses).

It's the man page section number. I believe this dates back to when the man(uals) were actually printed out. You'd go to section 2 to find X to disambiguate from a different Y.

http://www.december.com/unix/ref/mansec.html