Q:

What is role of palladium in hydrogenation reactions?

Why is palladium used in hydrogenation reactions? Is there any theory about the role of palladium and other catalysts in those reactions?

A:

The general catalysis cycle of hydrogenation reaction is pretty simple and AFAIK well documented. It consists of for reactions, all well documented in metalloorganic chemistry.

Hydrogen activation. It comes in many flavors, but idea is the same: $\ce{H-H}$ bond is broken and instead $\ce{M-H}$ bonds are formed. 
Alkene bonding with a metal center
Alkene insertion in $\ce{M-H}$ bond, forming $\ce{R-M}$ alkyl bond
Elimination of alkane from $\ce{R-M}$ and $\ce{M-H}$ fragments.

This general process can occur on mononuclear or polynuclear complexes and on metal surface. However, when selecting particular metal for the process it is important that the intermediate particles were neither too stable, or they will cover catalyst completely and remain there, nor too unstable or the process won't happen. It so happens, than Ni, Pd, Pt are in the sweet spot with Pd being one of the best. They are not, however, the only hydrogenation catalysts in existence, they are simply the ones with high activity and simple composition. For example, $\ce{Ni}$-promoted $\ce{WS2}$ catalystalso has significant hydrogenation activity.

A:

According to Wikipedia, it appears that the catalyst simply forms temporary bonds with both reactants, enabling said reactants to react with each other much faster than if they were just floating around. Palladium and other expensive metals are used as the catalysts because they are faster and more efficient than other ones which use cheaper materials.

The unsaturated substrate is chemisorbed onto the catalyst, with most sites covered by the substrate. In heterogeneous catalysts, hydrogen forms surface hydrides (M-H) from which hydrogens can be transferred to the chemisorbed substrate. Platinum, palladium, rhodium, and ruthenium form highly active catalysts, which operate at lower temperatures and lower pressures of H2.

