Why does a planet rotate and revolve? Why do planets rotate and revolve in the universe?
As the planets evolve during their protoplanetary stage and accrete materials from the protoplanetary disks, which are gravitationally collapsing interstellar dust and gases, these accreted particles retain some of the angular momentum from the materials they form from and being in constant motion.

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&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Generated image (virtual fly-by) from a simulation of the accretion period of the protoplanetary disk, showing preservation of&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;angular momentum in the orbit around a Jupiter-size planet, as it clears its neighborhood. (Source: Frédéric Masset)

One nice description for this angular momentum preservation, and why the planets appear to rotate faster than their surrounding protoplanetary disk goes like this:


  Conservation of angular momentum explains why an ice skater spins more
  rapidly as she pulls her arms in. As her arms come closer to her axis
  of rotation, her [rotation] speed increases and her angular momentum remains the
  same. Similarly, her rotation slows when she extends her arms at the
  conclusion of the spin.
  
  Source: Scientific American article on Why and how do planets rotate? (George Spagna)


So it could be described as this axial rotation of planets resulting in conservation of the angular momentum of the materials in the protoplanetary disk, forming during the accretion period of the planetary system as the protoplanets gain in weight, and preserve this angular momentum due to inertia of their radial velocity.