Being underwater a little is not all that scary, but those who talk of being underwater are typically underwater by quite a lot. The amount of money they owe is large compared to their yearly income.
Consider a metaphor. I put you in a hole. Its only 1 foot deep. You're not too concerned. If you want to leave, you can step out of it. Now we look at a deeper hole, 3 feet. Now you're still not too concerned. You can't just walk out, but if you need to get out you can wiggle your way up. 6 feet. Now you start getting nervous. Climbing out is getting trickier and trickier. You may not be able to move in response to a changing enviornment around you, because you're stuck in a hole.
Now make the hole 10 feet. Now you can't reach the edges. Now you're in trouble. You have lost all mobility. You can't get out under your own power. Now if something bad happens (such as losing your job or a sudden health issue), you can't move around to solve the problem.
This is the issue that arise from underwater mortgages. Say you lose your job because the job market in your area dried up (think Detroit in the big auto manufacturer crash). You need to move. You are legally endebted to a lender for your existing underwater house by more than you can sell it for. You need to pay for the privilege to sell it. You still owe payments on it, so if you just buy a new house (or rent) in the new state, you're paying for twice as much property. You can't just shuffle the underwaterness from your old house to your new house because the new lender has no interest in giving a loan for more than the value of the new home.
The only options you have to play with is renting the old house, which many underwater families did, or bankrupcy. If the area you were in is depressed, you may not be able to rent the house for enough to cover your mortgage. This is the fear of being underwater. You have a piece of paper which claims some lender can take money from you that you may or may not have, and that the US government will allow them to take your assets, if need be, to settle the score.
If you're underwater by a few thousand, it's typically not a big deal. If you're underwater by 80 or 90 thousand dollars, which some people were, that's a lot of money to be endebted for without the assets to recover them.
If you subscribe to the realtor story that the market will recover, all you have to do is scrape by, holding on, until the market rises again. However, those who are underwater recognize that the reason much of this occurred is that we entered a bubble because realtors kept saying the market could only go up. Fool me once....