First you need to know what are Signals in Unix-like systems (It'll take just few minutes).
Signals, are software interrupts sent to a (running) program to indicate that an important event has occurred.
The events can vary from user requests to illegal memory access errors. Some signals, such as the interrupt signal, indicate that a user has asked the program to do something that is not in the usual flow of control.
There are several types of Signals we can use - to get a full list of all the available/possible Signals use "$ kill -l" command:
In the above output it's clearly visible, that each Signal has a 'signal number' (e.g. 1, 2, 3) and a 'signal name' (e.g. SIGUP, SIGINT, SIGQUIT) associated with it. For a detailed look up what each and every Signal does, visit this link.
Finally, coming to the question "Why number 9 in kill -9 command":
There are several methods of delivering signals to a program or script. One of commonly used method for sending signal is to use the kill command - the basic syntax is:
$ kill -signal pid
Where signal is either the number or name of the signal, followed by the process Id (pid) to which the signal will be sent.
For example - -SIGKILL (or -9), signal kills the process immediately.
$ kill -SIGKILL 1001
and
$ kill -9 1001
both command are one the same thing i.e. above we have used the 'signal name', and later we have used 'signal number'.
Verdict: One has an open choice to whether use the 'signal name' or 'signal number' with the kill command.