What is a Floodplain?
Floodplains are large expanses of alluvium deposited by the decrease in river flow speed when rivers flood. Grain sizes of floodplain deposits vary from clay to gravel.
As rivers meander through a relatively flat area, they erode sediment at the outer edge of any curves. This lateral erosion caused by snaking meanders creates a flat valley over time.
When a river floods, the area the water is flowing through increases exponentially. As the water breaches its bank, it escapes into the rest of the valley. The water is unable to maintain the speed it was going before, and it slows down. As water slows down it can no longer keep sediment grains in transport, and it deposits them. Every time a river floods, it deposits the sediment it was carrying outside its boundaries. Over time, the flooding river replenishes a significant amount of sediment into its valley, building up the sediment. Eventually, the deposits from the flooding river may form a levee tall enough to keep the river from overflowing in that area.
Meandering Rivers https://geo.libretexts.org/Courses/University_of_California_Davis/UCD_GEL_109%3A_Sediments_and_Strata_(Sumner)/Textbook_Construction/Meandering_Rivers
Some rivers in flat areas flow in windy patterns, called "meanders" that form flood-plains and oxbow lakes. There is an entire page about them if you click on the link above.
What is an Oxbow Lake?
A "C"-shaped lake that was once part of a meander that got cut off. The still-standing water of the small lake is eventually filled with mud, leaving behind fine-grained mud overlying channel deposits.
Oxbow Lake Formation
As rivers erode on the outside of a curved section of river, two meanders (the curved part) can erode and move the outside of the river until two loops connect with each other. The river uses the shortcut and the loop that got cut out stays as an oxbow lake until it eventually fills with mud and dries up or the river meanders back to it again.
Below is a .gif of Landsat imagery that shows the evolution of a river in a floodplain and the formation of an oxbow lake as the river meanders.