Look at the amount of "fill" in the voids, or pores, of the travertine tile. This is the biggest indicator of quality. Tiles that show a large amount of filled voids are poorer quality and more likely to be brittle. High quality travertine has very few voids, is extremely dense, and will last a lifetime.
Observe the uniformity of the travertine tile's color. High-quality travertine has uniform color and markings, with very little color variation between tiles. It's much like hardwood flooring -- high quality woods have uniform grain patterns. If there is a large variation of color between tiles, it's lower-quality travertine.
Check for uniformity of tile size and thickness. When stacked, the tiles should be cut to the same size. When viewed from the side, width should be equal as well.
Look for unusual mineral deposits in the travertine's surface. High-quality travertine is mined from pure veins that are deep in the quarries, and have very few deposits of other minerals. Lower-quality travertine is mined from areas of the quarry that have been infiltrated by other types of stone and minerals, giving it a blotchy look.