It’s something HP build on to their machines and it does all the automated updates to HP BIOS and other hardware in your computer. It can do automated troubleshoots and fixes, too, but only on software, of course; if your hardware is kicking the bucket then there’s nothing it can do about that.
On those smaller, cheap machines with a ridiculously small SSD it’s a pain as every square gnat’s todger of space on that SSD is at a premium, and by the time people have finished bonging Norton, McAfee, or Kaspersky on there and then (sigh) banging on MS Office as well, that disc becomes non agaricus bisporus.
If you’ve got a decently-sized storage medium in there, it won’t do you any harm and might one day do you a bit of good, so leave it on, but stop it starting up when Windows does because then you’ll just get it gobbling resources in the background. You can still start it manually. Personally I let it start and then go round ending the task, but that’s a bit of a pain for most users.
Note: HP Support Assistant is accessed by clicking the blue question mark on the taskbar or, in Windows 8, through the HP Support Assistant app on the Start screen. If neither of these options work, you can also find it by clicking start and typing HP Support assistant.