I'm not sure I consciously thought about what raising the stakes meant until recently. When it comes to screenwriting, I learned this summer that you have to torture, torture, torture your protagonist. Whenever you can, turn the screws. I think this rule applies to comedy as well--perhaps even more so. Larry Gelbart used to advise writers to always put the protagonist somewhere s/he doesn't want to be, even if it was something as simple as in an army boot with a big hole, walking through the rain.
At any given time, a character has an intention (I want something) and an obstacle (something/someone is in the way of my getting it). When we ask the question "What is at stake?" we're asking the character what will happen if s/he doesn't get what s/he wants (or, perhaps, what happens if s/he does). Put another way, "What have you got to lose (or gain)?" If there's very little at stake--a bruised ego, a slap on the wrist, etc., then the reader is going to lose interest in the story, as well as the character. Raising the stakes means taking your characters to the brink-- losing a job, a home, a relationship. Becoming a fugitive, a refugee, an exile. Or perhaps it's gaining a child and not being able to afford to take care of her, or winning the lottery at the expense of losing a friend. Perhaps it's coming face to face with death.
Torture, torture, torture.
Knowing what's at stake will inform how or why our characters behave the way they do. When we raise the stakes, our characters enter the Point of No Return. They're forced to make choices that cause anxiety. They have to do things differently. And that's what keeps our readers riveted.
As a revision exercise, take two scenes from your draft -- your best one and your worst one -- and study the action of that scene. Is there an intention? Is there an obstacle? Is your protagonist somewhere s/he doesn't want to be? Determine what's at stake. Then turn the screws -- raise the stakes and see how your character responds. What happens?
I can't wait to find out.