A sponge on a stick is a small sponge fixed to a wooden or metal handle, and it exists for one problem: water pooling in the bottom of a thrown form too narrow for a hand. Left there, it softens the base and the pot cracks or slumps.
Why the water matters
Throwing puts water inside the form and it collects in the base, where the clay is thickest and slowest to dry. Water sitting there keeps the base soft while the walls stiffen, which distorts the pot when it is lifted and cracks the base as it dries unevenly. Getting it out before the pot leaves the wheel is a ten-second job that saves the piece.
Narrow forms
On a bowl you can reach in with a sponge in your fingers. On a bottle, a vase or anything with a narrow neck you cannot, and the sponge on a stick is the only way to reach the base without deforming the wall. That is the reason it exists and the reason every studio has one despite it looking like a trivial tool.
Other uses
Wetting a specific area without soaking the whole pot, cleaning slip from inside a form, and smoothing an interior curve that fingers cannot reach. It is also useful for damping a rim under plastic during slow drying, where reaching in with a hand would mark the wall.
Buying or making one
They cost very little and are sold by every supplier. Making one is trivial: a small natural or synthetic sponge tied or screwed to a length of dowel. Either way, wash it out rather than leaving it loaded with slip, because a sponge left full of clay hardens and stops absorbing.
Questions people ask about sponge on stick
What is a sponge on a stick for?
Removing water from the base inside a narrow thrown form, where a hand cannot reach without deforming the wall.
Why does water in the base matter?
It keeps the base soft while the walls stiffen, which distorts the pot when lifted and cracks it as it dries unevenly.
Can I make one?
Yes, a small sponge fixed to a length of dowel does the job. They are also cheap to buy.