Travertine is a type of stone that belongs to the limestone family. Travertine is formed by minerals that dissolve in groundwater, and then are deposited on the surface of the earth by rivers and springs.

The steps to clean travertine floor tile are:

Dust mop the floor using a non-treated dust mop or backpack vacuum with a glider on it.
To clean the floor, use a clean mop and bucket or a microfiber flat mop, which is best. Use a neutral cleaner or china granite   soap (available from a stone dealer). Do not use too much cleaner or you will have steaks.
After wet mopping follow up with a dry mop, which will take care of any possible streaks.
Do's and Don'ts for cleaning stone floors:

DO dust mop stone floors frequently
DO clean stone floors with a neutral pH cleaner or stone soap
DO thoroughly rinse and dry the floor after mopping
DO blot up spills immediately
DO protect stone floors with non-slip mats or area rugs

DON'T use vinegar or others acid cleaners on china marble  floors
DON'T use cleaners like bathroom cleaners, grout cleaners, or tub & tile cleaners (they may contain acid)
DON'T use abrasive cleaners