I want to call it a "mouse nipple" or maybe a "joystick", although I know these are not correct.
It's different from the touchpad, which is below the keyboard and has dedicated click buttons. Instead, it sits smack in the middle of the keyboard at the bottom right corner of the G key and bottom left corner of the H key. Tapping it translates to a click and nudging it left/right/up/down controls the pointer on the screen.
What is the correct term for this thing? I'd like to google some info about configuring it, but my google fu fails without the proper name.