I wouldn't say it's too complicated, but it is a weird show with a lot of off-the-wall ideas. Whenever someone asks me to explain the show, I keep it as simple as possible. "It's about a time travelling alien who visits Earth in its various eras." The only thing to ever cause confusion is explaining the Doctor's name.
"He's named the Doctor, not Doctor Who."
"Then why is the show called Doctor Who instead of The Doctor?"