finishing a tile to tile edge
Caulk.   Something that matches your floor grout is preferred so go with a regular or even sanded colored silicone caulk (I have used this).   I did notice that some of the tile is butted on the other tile and some with a good 1/8-1/4" gap.   I would lay a layer of caulk down on the large gaps flat to tile.   Let it dry two days then put a layer that is beveled throughout so that you have about 1/8" bead on the "top" of each tile piece.