Induced power is te power required to overcome Induced drag. Essentially this is the drag created by the act of producing lift and includes the effects of tip vortices as well as the work imparted to produce the induced flow that creates thrust.
Profile power is that required to overcome profile drag. This is created by the physical act of dragging a body through a viscous fluid, with the attendant friction etc.
The former decreases with speed, the latter increases.