Choose "Draw Tiles" if you want to edit the tiles in this tileset.

Choose "Cut Tiles" if you want to copy tiles from another tileset or extract tiles from an imported background.

Choose "Set Default Passability" if you want to define default walls for each tile in this tileset.

Choose "Define Tile Animation" to create patterns for animated tiles.

"View with background" specifies how color 0 is drawn, and affects the tileset editor only (it does nothing in-game!) When a tileset is used for map layer 1 and higher, color 0 is transparent, but on layer 0 it isn't!