it is a relatively dense polyurethane, with a good protective/strong but light fiberglass like coating to protect it from the weather and keep hail from damaging it when it sits out in the weather.
Hurled at hundreds of mph, it probably could do some pretty good damage.
Here's what I found about the tiles:
http://www.howstuffworks.com/question308.htm
The space shuttles are protected by special silica tiles. Silica (SiO2) is an incredible insulator. It is possible to hold a space shuttle tile by the edge and then heat up the center of the tile with a blow torch. The tile insulates so well that no heat makes it out to the edges. This page discusses the tiles:
Aerobraking tiles are produced from amorphous silica fibers which are pressed and sintered, with the resulting tile having as much as 93% porosity (i.e., very lightweight) and low thermal expansion, low thermal conductivity (e.g., the well known pictures of someone holding a Space Shuttle tile by the corners when the center is red hot), and good thermal shock properties. This process can be readily performed in space when we can produce silica of the required purity.
And from another site:
http://www.personal.psu.edu/faculty/r/8/r81/055/space_shuttle/shuttle.html
Shuttle orbiters use a system of 30,000 tiles made of a silica compound that does not ablate, but does rapidly radiate heat away from the orbiter. These tiles can be repaired in space. Major disadvantages are fragility (tiles easily damaged before launch and by orbital debris -- lots of tile damage due to debris since anti-satellite tests in mid-80's) and complexity (many people needed to manually attach tiles to orbiter in a tedious and time-consuming process, and to inspect them all before launch).
It's the easily damaged part that is of interest here. Note they can also be repaired. It would seem logical that every flight would include a space walk to ensure the integrity of the tiles.