$SIG{HUP} is the handler for the hangup signal which is sent to a process when it loses its controlling terminal. That happens, for instance, when a user logs out with a process running in background. A daemon process has no controlling terminal, so SIGHUP is available and is by custom used to tell the daemon to re-read its configuration files and re-initialize.

$SIG{TERM} is the handler for the process termination signal.

See man 7 signal for a list of signals and their default handlers. In most cases the system's default handler is sufficient and you don't need to write one of your own. It's best to not introduce unusual signal handling.