-9 is the signal number (in this case SIGKILL), so kill -9 sends a SIGKILL to the process in question.
This signal causes the process to terminate immediately (unless it's waiting in a kernel function). The signal can neither be ignored nor can the receiving process perform any clean up action after receiving the signal (i.e. a signal handler for SIGKILL is not called). See also the Wikipedia article on SIGKILL.
From the man page of my kill command (Linux):
The default signal for kill is TERM. Use -l or -L to list available
signals. Particularly useful signals include HUP, INT, KILL, STOP,
CONT, and 0. Alternate signals may be specified in three ways: -9
-SIGKILL -KILL.
EDIT:
kill -l (the bash built-in command) lists the following signal names and numeric values on my system:
1) SIGHUP 2) SIGINT 3) SIGQUIT 4) SIGILL 5) SIGTRAP
6) SIGABRT 7) SIGBUS 8) SIGFPE 9) SIGKILL 10) SIGUSR1
11) SIGSEGV 12) SIGUSR2 13) SIGPIPE 14) SIGALRM 15) SIGTERM
16) SIGSTKFLT 17) SIGCHLD 18) SIGCONT 19) SIGSTOP 20) SIGTSTP
21) SIGTTIN 22) SIGTTOU 23) SIGURG 24) SIGXCPU 25) SIGXFSZ
26) SIGVTALRM 27) SIGPROF 28) SIGWINCH 29) SIGIO 30) SIGPWR
31) SIGSYS 34) SIGRTMIN 35) SIGRTMIN+1 36) SIGRTMIN+2 37) SIGRTMIN+3
38) SIGRTMIN+4 39) SIGRTMIN+5 40) SIGRTMIN+6 41) SIGRTMIN+7 42) SIGRTMIN+8
43) SIGRTMIN+9 44) SIGRTMIN+10 45) SIGRTMIN+11 46) SIGRTMIN+12 47) SIGRTMIN+13
48) SIGRTMIN+14 49) SIGRTMIN+15 50) SIGRTMAX-14 51) SIGRTMAX-13 52) SIGRTMAX-12
53) SIGRTMAX-11 54) SIGRTMAX-10 55) SIGRTMAX-9 56) SIGRTMAX-8 57) SIGRTMAX-7
58) SIGRTMAX-6 59) SIGRTMAX-5 60) SIGRTMAX-4 61) SIGRTMAX-3 62) SIGRTMAX-2
63) SIGRTMAX-1 64) SIGRTMAX
-9is an instance of-sigspec, it's equivalent to-s 9or-n 9or-s KILLor-KILL. – Gilles Jun 19 '11 at 10:18