1x1, 2x2, and 3x3 sample tiling
The tiling pattern you set with this option affects only the sample slot. It has no effect on the tiling on the geometry in the scene, which you control with parameters in the map's own coordinates rollout.
The buttons specify the number of times the pattern repeats over the surface of the sample object. Because maps are mapped spherically around the sample sphere, the tiling repetition covers the entire surface of the sphere. The sample cylinder maps cylindrically. The sample cube uses box mapping: the tiling appears on each side of the cube. Custom sample objects use the default mapping coordinates for that kind of object, unless the object has a UVW Map modifier applied to it, in which case the modifier controls the mapping.
This flyout is unavailable when the sample slot displays a standalone (top-level) map.