The listing of a directory shows certain files with permissions set to rwsr-xr-x. what does this indicate?

"rws" means that the user has permissions to read, write and setuid. "r" means the user can read the file and "w" means that the user can write to the file. "s" stands for "setuid" (set user id) is a permission bit that allows the users to execute a program with the permissions of its owner. The "s" can also mean "setgid" (set group id) is a bit that allows the user to execute a program with the permissions of the group owner.