Obviously none of these terms are set in stone. But in general this is what they seem to imply:
Reboot: Complete reimagining/reset of the game/series with an all new story, characters and gameplay, but often with a couple of returning elements that make the series unique. For example the newer Tomb Raider games.
Remake: Taking an older game and completely remaking it from scratch. All new gameplay, graphics and engine. Pacing of the story is often changed, and characters may be expanded. For example the Resident Evil 2 or Final Fantasy 7 Remake.
Remaster: Taking an older game and giving it a facelift, improving the engine, improving graphics, adding some quality of life features and expanding and fixing gameplay issues. However 9/10 times it's just marketing term for lazy next-gen console ports where they added some shitty new lightning effects and outsourced 3D models so they have to excuse to charge 60 bucks for it. Most remasters also run on the same engine as the older game.