Cursed with awesome
The DM PC or Dungeon Master Player Character is really an NPC that acts like a PC: going on adventures, saving the day, and often upstaging the actual PCs. Because the GM of the game cannot play the character they want, they often instead insert a character for them to play into the story. At their best, they can be beloved supporting characters or foils for the party, and at their worst they can be glory hogs always saying the party like the worst deux ex machina since Odin and Zeus got bored and decided to walk the earth helping strangers and righting wrongs with their monkey sidekick.
The archetypal DM PC tends to be Elminster from the Forgotten Realms and Ed Greenwood has taken a lot of heat for that – even though the character wasn’t designed around that purpose. The excellent DM of the Rings webcomic also makes great use of the trope with Gandalf.
Funny, our DM’s PC has little to no character backstory/development and purposely takes a backseat to the PCs. The most exciting thing that he has done is try to con us out of a gem by understating its value. The NPCs are more overpowered, but my 9 WIS character thinks they might be evil.
I sneak mine in as guide-type characters. They end up working much like butlers or familiars – you only vaguely realize they’re there, then when they’re gone and the players go “Okay, so I’ll cast a few abjurations, you sneak around behind it, and the GM will… Oh wait, his character pulled a Gandalf an hour ago.”