When you install tile over concrete foundations keep a keen eye out for hairline cracks. Cracks like this one is an indication of slab movement. If the slab moves any more (very likely since it is cracked) it is likely that the crack will transfer through the surface of the tile.
To prevent the crack from appearing on the tile surface, install crack isolation membrane over the crack in the slab. Crack isolation membranes are available at any home improvement store and are fairly inexpensive (especially when taking into account the cost and time of replacing a tile). Crack isolation membranes will allow the surface under the tile to shift slightly without transferring that shift through your tile surface. Proper installation of crack isolation membrane is extremely important and easy to do. You know your time is well spent when you don’t see that crack come through your tile.
If you have tile with cracks in them it is likely that you have hairline cracks in your slab. When you replace the cracked tiles, simply clean the crack in the concrete and use the crack isolation membrane prior to installing your replacement tile. Again, if you see a hairline crack in any surface prior to installing tile, make sure to isolate the crack to prevent it from showing up in your tile surface. Let me know if you have any questions.