Faster on the outside
Any small deflection sends the fastest thread of water to the outer bank. Faster water erodes more, so the bend deepens itself.
Slower on the inside
On the inner bank the water slows and drops its load, building a slip-off slope of sand and shingle. Erosion on one side, deposition on the other.
Meanders and oxbows
Bends migrate downstream over decades. When two bends meet during a flood, the river cuts across the neck and abandons the loop as an oxbow lake.