Phrase Meaning – What’s the Meaning of “Old Hob”?

Good old is whatever is liked or admired or familiar and comforting which

• remains from the past, still functioning as it always did

  My good old 63 Cutlass
  Good old Jimmy Carter
  The good old Chicago Democratic machine

• existed or obtained in the past (or you believe existed or obtained in the past) -- the "Good old days" -- but is now neglected or vanishing or gone

  The good old tradition of liberal education
  The good old portable typewriter

However, the term is almost always used ironically today:

Good old Bob, always finds a new way to screw it up.
Good old VHS had absolutely unique reds and oranges.
The good old Know-Nothing party seems to be making a comeback.

Good old boy is a specialized application of the term: a well-regarded and 'connected' man of the politically dominant yeoman class in the US South. This must be distinguished from the British old boy, originally an alumnus of one of the prestige 'public' schools, by extension a well-regarded and 'connected' man of the political and financial elite. The two exhibit very different manners and mannerisms.

Literally it refers to "checking out of a hotel." It's something you do when you leave the hotel. Once you've checked out, you're gone.

This can be used figuratively in a few ways. The basic metaphor is that once you've checked out, you're gone. It could mean several things:

1. Death. It's what you do when you leave this mortal life behind. Once you've checked out, you're gone.

2. Senility. If you're still here physically but mentally you've checked out, then your body is still here but your mind is gone.

In your example, it's like #2 but perhaps without the sense of permanence. Physically speaking, you're sitting in class or you're at a meeting, but mentally speaking you're not there at all. It doesn't appear to suggest actual senility in this case, though—it's just being used to describe a lack of attention. This seems to me like a slightly more extended use of the metaphor.