Flat, grey semi smooth stone.
Like sandstone but harder.
Most outdoor nurseries carry some and sell by the pound. Generally it will last forever once you find the right sized peice.
Like mentioned above, you can use overturned floor tiles (shiny side down) or several other things for nail and beak maintenance including terra cota plates.
I use cement pads throughout my enclosures. For feeding and as a pathway.
All soft substrate will not help with nails and beak maintenance. A few flat, semi rough areas are helpful. But make them flush with the rest of the substrate so that your tortoise will not scrape its underside (carapace) as is walks over the area.
I assume you also wanted to know why some of use recommend using slate.