Why do floodplains often contain fertile soil?

When floods run down they also bring a lot of organic material along with them. Floods also tend to grind up stones/sand to a certain degree.

Where the flood deposits this material it helps fertilize the soil.

A lot of water keeps the soil very moist, which also increases the rate of organic material to decompose (Bacteria and various insects/larva and of course also fungus does this)

Decomposed organic material are the building blocks for new plant life.

As we humans eat dead animals (Meat, although not decomposed), plants "eat" or rather suck up the nutrition from the decomposed material left around.