Chemical function of Mg and Conjugated bonds in Chlorophyll
but why do conjugated bonds increase this ability


Adsorption of light results in excitation of an electron, moving from low-level (usually bonding or non-bonding) to a higher (usually antibonding) orbital. (for understanding of what bonding, non-bonding and antiboding orbitals are, see here)

Generally, when two orbitals of same energy partially overlap, two more are formed: one with slightly higher energy and one with slightly lower. When orbitals of conjugated bonds interact, energy of one bonding orbital goes up and of one antibonding orbital goes does, narrowing the gap. When the gap is withing or closely near ~1.6-3.2 eV it can participate in visible light adsorption.


  this molecule does not seem to be have any resonance structures


It does, see carefully.


  what role does this metal complex serve in the molecule


The relevant metal-free molecule do exist in nature. It has, however, different color. $Mg$ ion seems to adjust the gap mentioned above. For a more clear understanding of the matter you might look for data on phtalocianin pigments, that may be easily obtained with different central atom in a very similar structure.