The rights a user has to do things to files or objects. In *NIX there are 3 basic permissions available, read, write, and execute. A file permissions may look something like:
-rwxr-x--x
The first character is used for special permissions (ex: link, directory, sticky-bit). The next three are your permissions (rwx), characters 5, 6, and 7 are group permissions, and 8, 9, and 10 are for everyone else. Other Operating Systems / Network Operating Systems have other rights.