Why is wave particle duality important?
Thanks for the excellent question!
Photons exhibit properties both of energy and matter. They do have mass (Compton proved they do have mass, even though it is VERY small ).
Proof that they behave like energy is that photons exhibit interference; they cross over each other and do not knock each other out of the way.
The photoelectric effect proves that photons can be quantitized like matter. Red photons do not have as much energy as blue or violet photons of visible light.
Thus, photons have a dual nature exhibiting properties of both energy and matter. They are really strange and useful!!
Hope this helps.