What does "back up" mean in this dialog?

Solution 1:

From Merriam-Webster's definition of back:

1 : to move backward
// backed into a parking space
—often used with up
// back up to give him some space
// Let's back up a little to clarify what we're saying.

It's the final example sentence that is most relevant to your passage.

To paraphrase and provide alternatives:

Let's move backwards from the more general case.
Let's back away from the more general case.

→ Let's back up from the more general case.

It's being used figuratively, not literally.

You asked, "Does it mean the Professor wants to use something more general to support his point of view?"

No, it's the opposite.

Restating the actual sentence, but adding my own emphasis:

If we take a resource like water . . . well, maybe we should get a little bit more specific here—back up from the more general case—and talk about underground water in particular.

So, the professor wants to use something less general and more particular. In other words, rather than talking about water as a whole, they want to talk about underground water specifically.