brss01a.exe is a process which is used by the Brother Print Processor (the Brother Print Processor is an integral part of most Brother printer drivers). Terminating these processes will cause your PC to not be able to communicate with the Brother device if it is connected via the Parallel, USB or network interface.
"This program is a non-essential process, but should not be terminated unless suspected to be causing problems. "
Non-system processes like brss01a.exe originate from software you installed on your system. Since most applications store data in your system's registry, it is likely that over time your registry suffers fragmentation and accumulates invalid entries which can affect your PC's performance. It is recommended that you check your registry to identify slowdown issues