That is a meaningless question. All we can do is observe and measure it's effects. Causes and meanings are epiphenomena.

The momentum p of a photon is determined by dividing its energy by the speed of light, or

p = E/c

The energy E is determined by multiplying its frequency "nu" (sorry my keyboard don't know Greek) times Planck's Constant h, so

E = h nu.

These equations did not just come out of thin air, they were predicted by theory and confirmed by experiment. You will note no mass term appears anywhere here.

The momentum of a photon is important since momentum is conserved and by assigning a momentum to the photon any interactions it will have with other particles can be predicted and calculated because we know the momentum before and after the interaction will be the same.

For example, a photon emitted by an accellerating electron will have to be of an energy such that the total energy of both particles as well as their total momentum will be the same both before and after the interaction. This necessarilly will place constraints on the frequency of the emitted photon.

Extra Credit:

One peculiar result of photon momentum is it's use in light sails. If a light sail is painted black, and it absorbs a photon completely, the total momentum p of the photon will be transferred to the spacecraft causing it to speed up. Total momentum is the same before and after the interaction, and it has a value of +p, all now in the spacecraft.

However, if the sail is painted with reflective paint, the photon will be reflected and the momentum of the reflected photon will be -p. For the total momentum to be conserved at it's initial +p value, the momentum transferred to the spacecraft must now be 2p. (2p - p = p). In other words, your sail is twice as efficient if it is highly photon-reflective, and not photon absorbing, just the opposite of what you'd expect.