Each process is controlled by sending signals to it which tell it what to do. This is how the kill command has its effect; by sending a process a signal which tells it to stop, hang up or terminate etc.
You can list the different types of signal that can be sent to a process by using the kill command together with its -l option. For example:
kill -l 1) SIGHUP 2) SIGINT 3) SIGQUIT 4) SIGILL 5) SIGTRAP 6) SIGIOT 7) SIGEMT 8) SIGFPE 9) SIGKILL 10) SIGBUS 11) SIGSEGV 12) SIGSYS 13) SIGPIPE 14) SIGALRM 15) SIGTERM 16) SIGUSR1 17) SIGUSR2 18) SIGCHLD 19) SIGPWR 20) SIGWINCH 21) SIGURG 22) SIGIO 23) SIGSTOP 24) SIGTSTP 25) SIGCONT 26) SIGTTIN 27) SIGTTOU 28) SIGVTALRM 29) SIGPROF
Signal type 1 (one) will send a process a signal to hang up (SIGHUP): signal type 9 (nine) is a signal to kill (SIGKILL) the process. This is certain to kill it.