The pressure drop is a macroscopic manifestation of a microscopic phenomenon. Molecules in the fluid give up energy as they shear past the walls of the pipe and past other molecules in the fluid. We could gain a better understanding of this shearing if we could view the motion of the molecules in the fluid, or view the motion of small packets or chunks of fluid as it travels down the pipe.
When a Newtonian fluid flows through a pipe it dows not move at a uniform velocity (plug flow). Instead, fluid near the walls of the pipe will move more slowly (because of friction with the pipe walls) than fluid near the center of the pipe. The velocity profile is the velocity of each infinetesimal chunk of fluid in the pipe. You can also think of the velocity profile as representing the velocity of the individual molecures in the fluid.
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