kill just sends a signal to the given process. The -9 tells it which signal to send.
Different numbers correspond to different common signals. SIGINT, for example, is 2, so to send a process the SIGINT signal issue the command
$ kill -2 <pid>
The manpage here specifies:
The default signal for kill is TERM.
The manpage also provides a table of signals you can send. According to this table, TERM is 15, so these are all equivalent:
kill <pid>
kill -15 <pid>
kill -TERM <pid>
Notice 9 is the KILL signal.
Name Number Action
-----------------------
ALRM 14 exit
HUP 1 exit
INT 2 exit
KILL 9 exit this signal may not be blocked
PIPE 13 exit
POLL exit
PROF exit
TERM 15 exit [Default]
USR1 exit
USR2 exit
VTALRM exit
STKFLT exit may not be implemented
PWR ignore may exit on some systems
WINCH ignore
CHLD ignore
URG ignore
TSTP stop may interact with the shell
TTIN stop may interact with the shell
TTOU stop may interact with the shell
STOP stop this signal may not be blocked
CONT restart continue if stopped, otherwise ignore
ABRT 6 core
FPE 8 core
ILL 4 core
QUIT 3 core
SEGV 11 core
TRAP 5 core
SYS core may not be implemented
EMT core may not be implemented
BUS core core dump may fail
XCPU core core dump may fail
XFSZ core core dump may fail