It is the cheapest thing you will buy for a rug and the one that decides how long the rug lasts. Almost nobody asks about pads. Almost everybody should, because a pad is doing structural work that the rug itself is not built to do.
What a pad actually does
Every footstep compresses the pile down onto whatever is underneath it. On a bare hardwood floor that compression is taken by the knots and the foundation threads. A pad absorbs it instead, and the difference over a decade of traffic is visible: padded rugs keep their pile height in the walking lanes, unpadded ones develop a flattened track.
It also stops the rug creeping, which matters for both the rug and the person walking on it. A rug that slides is a rug whose edges take repeated lateral stress, and edges are the most expensive part to repair.
“A pad takes the compression that would otherwise be taken by the knots. Ten years on, you can see the difference.”
What to buy
Felt-and-rubber. Felt for cushioning, a natural rubber backing for grip. It should be cut two inches smaller than the rug on every side so it disappears under the edges. Avoid anything sold as a cheap PVC or plastic mesh grid. Those degrade, and as they break down the plasticiser can migrate into a wood finish and leave a permanent haze on the floor.
Thickness depends on the floor. A quarter inch is right for most rooms; go thinner under a door that has to clear it, and thicker in a bedroom where you want the underfoot feel.