Sometimes when I'm running a killall command from Terminal, a co-worker would suggest or edit my scripts to show killall -HUP. What does the -HUP part do?
The -HUP option is the signal that's sent to the processes by the killall command. It can be a little hard to tell, but the relevant entry in the killall manual is:
The TERM signal (historically the "terminate signal") is usually sent to a program to request its termination (which is a politer version of forcing its termination with the KILL signal). The program is free to catch and ignore the TERM signal. It doesn't have to terminate if it doesn't want to and it can completely ignore this signal.
The HUP signal (historically the "hangup signal") is usually sent to a program to request that it restarts and re-reads all its configuration in the process. The actual behaviour of the program depends on the program-specific implementation. Not all programs catch HUP and they aren't required to by convention or dogma. For example, the Apache web server will catch a HUP signal and re-read all its configuration files but it won't restart any processes.
If you want to truly terminate the processes and not worry about whether they're going to catch and obey the signal uses the KILL signal. It cannot be caught or ignored and results in process termination.
For a good review of available POSIX signals see this Wikipedia article.