The no-slip condition occurs in viscous fluids when the fluid velocity is zero relatively to a solid surface. For example, imagine some liquid flowing in a pipe. If the velocity of fluid particles relative to the pipe walls is zero, this is the no-slip condition.
What causes this condition is the forces of intermolecular interaction. If the forces between the solid surface and fluid particles are greater than the forces of interaction between fluid particles, this will result in no-slip condition.