If a second current carrying conductor is placed near to the first and the corresponding magnetic fields drawn, we can begin to visualise why a force is created between them.

If the current in the wires are in opposite directions as shown here, the flux lines crowd between the wires tending to push them apart.                                 F ∝ I * B                              (cross product of vectors)

If the current in the wires are in the same direction as shown here, the flux lines flow around both wires and tend to pull them together.