Siltstone is made from silt of course. Silt is another name for clay and is very fine grained. The grain size is from 1/16 to 1/256 of a millimeter in diameter. It is very similar to sandstone in appearance but with a finer texture.
Once deposited the silt becomes compacted and cemented together into solid stone.
Silica, calcite, and iron oxides are the most common cementing minerals for siltstone. These minerals are deposited in the spaces between the silt grains by water. Over the course of thousands or even millions of years the minerals fill up all of the spaces resulting in solid rock.