Sure! I tried to indicate with the red and green lines hastily added in MS Paint, but the gist of it is when water goes around a curve, it doesn't flow perfectly in the middle. The majority of the water hugs the outer wall (the cutbank) and is traveling faster. As it's faster, it takes more sediment with it, thus deepening that part of the river. The deepest point in a river is part of a line called a thalweg. You can see it all summarized in the image below.
tl;dr: Water moves through a river kind of like a race car goes around a race track
Thank you for the explanation! I would however say it's the exact opposite of how a racecar goes around a track, because they try to take the inside of corners rather than the outside.