Those tiles did not adhere properly for one or more of several reasons: inadequate substrate preparation, inadequate or improper adhesive, adhesive not used correctly, etc.
My opinion is: not enough adhesive was used to bond the tiles. Also, the concrete may not have been made completely smooth and clean prior to installation.
There are two basic ways to bond that tile to concrete, the most common method is thin-set mortar (a cementitious tile adhesive), the second would be a pre-mixed tile adhesive sometimes called mastic.
- use a putty knife or margin trowel to assess how well all surrounding tiles have bonded (pry up just a bit, gently) and remove any additional tiles that are not properly bonded, as these will be likely to come loose soon if they hav not already.
- scrape all remaining adhesive and anything else from the concrete with a razor scraper, then wash concrete clean and let dry.
- remove as much old adhesive from the back of the tiles as you can (this will be difficult, especially since the tiles appear to be so small); if you have new matching tiles available then use those instead.
- install the tiles, following the directions for your chosen adhesive carefully (I would probably use the mastic because you will have a better chance of getting the tiles level with the surrounding field). I cannot tell how large those tiles are because there is nothing for scale in the picture, but it looks like mosaic so if it is and there are specific instructions for mosaic on the adhesive package, follow that.
- grout only after waiting appropriate time recommended on adhesive instructions.