Per your question, I understand you are not asking for detailed implementation code, since that would be asking for too much more than one single question can offer. So, I understand you are actually asking in conceptual terms.
That being the case, the first thing to tell you is that you can actually do both: you can have tile-based games both in 2D and in 3D. You can even have tile-based games that are programmed as 3D while looking as 2D (e.g. with a top-down camera over the 3D objects). And you can also have games programmed in a 2D logic but which appear to be 3D because of the angles of the objects that are displayed in the 2D sprites (sometimes these are called 2.5D tile-based games).
That being said, you can both use sprites in 2D and/or 3D meshes for a 3D tile-based game. Or you can even mix them. However, let me just give one further clarification. The sprites and/or 3D meshes are usually used for the 2D or 3D objects, respectively. Objects that occupy the tiles in the game-world.
But I always find it is easier if you think about the tiles in themselves as being the specific space that characters and objects can occupy and trough which they can move. These spaces can be of the shape of squares or hexagons, etc. These spaces can be filled with sprites or with 3D entities. Therefore, such spaces are previously defined in the code (this means to say the tiles can be merely given by the coordinates the objects can occupy/move trough. For Unity, see this tutorial on creating a square grid for future character movement: https://www.youtube.com/watch?v=nhiFx28e7JY).
I recommend you start by reading the following wiki entry: https://en.wikipedia.org/wiki/Tile-based_video_game
Later, search for tile-based games in the gamedev.net forums. There are tons of threads there with good conceptual debates (and even tutorials). And for the implementation of grids for character movement. Those can be of help to get you started, even if they are not tile-based specific.
Also, past questions in this very site can be of help to you. One is: Implementing a 3d tile engine