A tileset is a collection of palettes, tiles, combos, Door Combo Sets and sprites. It is intended to be imported into ZQuest so a quest designer has all the graphics needed to begin building a quest right away.
Tilesets can be imported/exported from the ZQuest Editor under the ZQuest Graphics pack extension .ZGP, but the preferred method of distributing a tileset is to use a .QST, also known as a Zelda quest. Normally, a full quest is saved as a .QST, or an Encoded Quest File. The majority of tileset makers out there, though, prefer to use a QST that is set up with tiles, palettes, combos, and other graphical aspects for the distribution of the set. The QST file can contain example shots to demonstrate the usage of the set. However, it is rarely playable in the Zelda Classic player and is not intended for doing so.
There are a large number of tilesets that have been created and are available on the web. Many are based on the graphics of Zelda games, such as Classic from The Legend of Zelda and A Link to the Past, edited to be usable in ZC. Others, such as the Pure tileset, are combinations of tiles from a large number of Zelda games and also include a few custom ones. There are also tilesets which are based on other games or are entirely custom, though they are fewer in number.