Rimstone Pools are formed by water flowing down a slope. A very thin layer of water on a rather big area has a large surface. Because of the large surface the water looses carbondioxide (CO2) to the atmosphere of the cave and as a result calcite precipitates.
The flowing water has waves on its suface, caused by irregulities of the rock surface. Thin waves form the precipitated calcite into arcs or curves like the wind formes sand dunes. If there is a rim formed this way, the rim hold a pool of water.
Still calcite is precipitated and accumulates on the water surface. When a larger wave occures the whole calcite is transported to the rim. It is clear, that most of the calcite is deposited on top of the rim.
Rimstone pools can not only be found in caves. There are several famous pools all over the world.
But there is a big problen on the surface: growing plants (moss and leaves) disturb the calcite precipitation. So there are huge travertine deposits formed, but now pools. Lakes like in Plitvice are formed the same way but look very different.
Rimstone pools on the surface are always build by thermal spring waters. The temperatur of the water kills the moss and allows the undisturbed growth of the rims.
Sometimes the rims consist of calcite, but very often there are also several silicates (minerals consisting of SiO2).