At the reflective walls of our universe, the fabric of space (see more about the ether on the last page of this website) is stretched further into curved lines that diverge into conical shapes, producing a repulsive force and an acceleration away from the wall.
This is the opposite of gravity. While the presence of matter distorts space so as to make converging lines in space and time to produce the field of acceleration that we call gravity, near the walls there is a repulsive force.

Approaching the boundary from a spaceship would be like approaching a mirror. You would see your own reflection some distance away until at some point, when you got close enough to the wall, there would be an increasing force pushing the ship back, like running into a soft spring that gets progressively stiffer. The closer you get, the harder it is to advance as more power is required. The ship would come to a stop when the driving force of the ship equaled the inverse gravity force at the boundary. In this sense, the boundary has a thickness associated with it. It is a boundary which we can never reach.

What the walls are made of will always be unknown. This is equivalent to the question of what is outside the current expanding universe model. We can guess that there is considerable tension on the walls but there are some things we can never know for sure.