The introduction to this article does not have enough information for people unfamiliar with the subject.
Laminar flow is characterized by the smooth flow of a liquid. This tends to happen at low velocities when there are few disturbances, such as in a straight, smooth pipe. In laminar flow through a pipe, it is assumed that the velocity of the fluid is zero at the boundaries of the pipe and is at a maximum in the center; mathematically, the velocity profile is parabolic. Microscopically, the particles or pieces of the liquid flow in a straight line along the direction of the pipe and do not mix with other layers of fluid. The layers slide past one another like playing cards. This is in contrast to turbulent flow, when a fluid swirls around.
Even though there is no mixing, there is still some friction in the flow. This friction will cause a pressure drop and its numerical value is given by the Hagen-Poiseuille equation.