Ceramic tile flooring is very durable and easy to care for if swept and damp mopped regularly. As a rule, hard scrubbing isn't necessary, unless the flooring is very old, stained, yellowed, or very dirty. At that point, you may need to use a stronger soap and scrub brush to get it completely clean. A natural bristle brush used only as vigorously as necessary is all that is needed.
If you are scrubbing the floor and a film comes off, it may be a varnish or sealant that has been previously applied to the flooring. It can be resealed after the flooring is dry. If the tile was glazed and a film comes off, you have damaged the tile and removed the protective glaze.