Unix file permissions control who can read, write, or execute files and directories in a Unix operating system. Each file has three types of permissions: read (r), write (w), and execute (x). These permissions can be assigned to three categories of users: the owner of the file, the group associated with the file, and all other users. Permissions are represented in a symbolic format (like rwx) or numeric format (like 755). For example, a permission of 755 means the owner can read, write, and execute, while the group and others can only read and execute. Understanding these permissions is essential for maintaining security and proper access control.