Physid snails, one of the so-called pond snails. The chances are they came in as either snails or eggs on your plants.
They breed more if they have a lot of food - uneaten fish food, algae in the tank. When they take over it's usually because the fish are being over fed. Fish need a lot less food than you'd think. The majority of our food goes to maintain our body temperature. Fish get their body temp from the water so they need a lot less food than we do, body weight for body weight.
If you want to get rid of them you could try a snail trap. For this you need a jar with a screw top lid. Punch holes in the lid from the outside so that the spikes around the holes point into the jar. The holes need to be big enough for snails to get through but small enough so the fish can't. Just before the room lights are turned off for the night, put lettuce into the jar and put the jar on the bottom of the tank. In theory, the snails will go into the jar to eat the lettuce and the spikes around the holes will stop them getting back out.