A sliver is a small artifact resulting from the boolean operation. Very often it is generated when subtracting a shape that was originally an arc. Slivers end up isolated from the main body. If the sliver option is checked, the program will check each polygon's sliver value and delete any that whose sliver value is less than the user specified setting.
In the snapshot below you can see a circuit board pad surrounded by groundplane with several tiny slivers in the group plane that were generated when the stroked fills did not exactly overlap.
The sliver value is defined by:
2 x Area
sliver value = -------------
perimeter
In the example above we can approximate it by a triangle with base 0.0002 inch and height 0.0035 inch. This gives a silver of
2 x 1/2 0.0002 x 0.0035
------------------------ = ,000097
0.0035 + 0.0035 + 0.0002
If the user selects a sliver parameter of 0.0001 or larger then this sliver will be removed.