To understand this at a simple level, take three formulas: E=mc², E=hf (h is Planck's constant) and the standard wave formula c=fλ.

You then get de Broglie's formula, λ=mc/h.

Now, mc is momentum, p, so that p=hλ.

This was used by de Broglie to suggest that massive particles, such as electrons, can show wave-like properties. In your case, this shows that a photon can have momentum and hence can create pressure.

This is all non-relativistic and as taught in upper secondary physics, but hope it helps.