It may very well be the the 3D analogue of the 2D surface of a sphere. We can walk all round the surface of the earth and never find a boundary, but the earth is only 8000 miles in diameter, far from infinite: finite and unbounded. The earth's surface is a two dimensional plane curving into a third dimensional volume.

The universe may be a three dimensional volume curving into a fourth dimensional hyperspace. If this is the case, there may be nothing "outside" it, just as there is nothing "outside" the earth's surface. Just as if you start walking on earth you eventually return to the same spot you started from but from the opposite direction, it may be that if you travel in space long enough you will simply return to the same spot you started at from the opposite direction.

In its simplest conception, the universe is a bubble of space time some 14 Giga light years in radius. There is no boundary, no edge, and nothing "outside" it. But when you start considering expansion of the universe, and hyperinflation during the big bang, and a host of other cosmological theories now floating around, it can get a lot more complex than that. In short, we don't know. But I'll bet you my next paycheck that if we ever do find out, the answer will be even stranger than we can think.