The main properties that Molybdenemum (usually along woth Cobalt and/or Nickel) has that makes it a preferred catalyst over more effective catalyst like Platinum and Paladium is that it is more abundent and therefore much expensive, it can provide a long stable and somewhat predictable run length and it is not easily poisoned.  It is "good enough" (usally in a sulfided form) at adsorbing S or N containing molecules (and even aromatics) stongly enough to significantly increase the chances of reacting with nearby/adsorbed H2 but weakly enough to desorb reaction proucts quickly.

Like most othr catalysts it is used because researchers tried it and found it to work and once the discovered it wotked (note they also tried lot of other things likethat didn't work as well) they continuously experimented mostly be trial and error to change metal content surface area acidity and other properties in an effort to improve performance.  There is almost always a good theoretcal w reason.why a new formulation should work better than previous formulations but in reality most new formulations fail.  The few that suceed often lead toward a direction for future improvements and hydroprocessing catalyst usually comtain Cobalt or Nickel and Molybdenum slowly continue to get better over time.

Thanks for the reply, Sir!

But, Is there any kind of exceptional behaviour of Molybdenum element that can help us understand any process of Nano/Quantum Level?

I don't know much more about the Nano/Quanum level structure of Molybdinum then what you can read in Wikipedia:

"MoS2 usually consists of a mixture of two major polytypes of similar structure, 2H and 3R. The former is more abundant.[5] In 2H-MoS

2, each Mo(IV) center occupies a trigonal prismatic coordination sphere that is bound to six sulfide ligands. Each sulfur centre is pyramidal and is connected to three Mo centres. In this way, the trigonal prisms are interconnected to give a layered structure, wherein molybdenum atoms are sandwiched between layers of sulfur atoms."

I do know that  Mo and MoO2 are not very good catalyst but MoS2 has some properties that make it a  good "Cocatalyst",  MoS2  requires another real catalyst like Ni or Co to make it effective.  I beleive that the MOS2 prinarily acts by adsording organic sulfur and nitrogen or aromatic compounds and keeping them close to the Ni or Co c=catalyst that actually catalyzes the hetroatom removal and aromatic saturation reactions.