Velocity is faster at the outside bend of a meander because that is where the channel is deepest and there is the least friction. By contrast, the inside bend of a meander is shallow and exposes water to more friction, slowing it down.
As a general rule, a river's current flows fastest where the channel is deepest and there are the fewest obstructions. When a riverbed contains a meander, the water moves in what is known as a helicoidal flow. In a helicoidal flow the main current corkscrews from one side of the river to the other, creating more erosion and carving out a deeper channel on the outside of the meander. On the inside of the meander, there is less erosion and a shallower riverbed. Because of this structure, the water on the outside of the meander has the deepest channel and the least friction, which causes it to move faster than the water on the inside of the meander where the river is shallower.
Because of the structure of the riverbed in a meander, the water continues to exaggerate the differences in depth between the inside and outside of the meander. Because the water on the inside moves more slowly, it deposits more sediment, making the inside of the turn shallower and slower. At the same time, the fast moving water continually erodes the outside of the meander, making the channel deeper and faster.