Role of amalgamated zinc in Clemmensen reduction
As the illustration below would show, you can use either amalgamated zinc  (in a Clemmensen reduction) or hydrazine (in a Wolf-Kishner reduction). This reaction as drawn hides some of the secondary products which should be zinc peroxide and mercury oxide*



Metallic zinc is “activated” by mercury by “dissolving” it into individual atoms of zinc that are distributed evenly in the alloy. You're basically creating a zinc solution.

The reaction of zinc with HCl releases hydrogen gas.
However, when this reaction takes place with zinc amalgam, the individual hydrogen molecules that are formed by the reaction of zinc with HCl remain in a reactive state (sometimes called “nascent hydrogen”) and reacts with the ketone to initiate the reduction reaction.

So the mercury in zinc amalgam serves to “trap” the active hydrogen as it is formed, and allows it to attack the carbonyl compound rather than be released as a gas.

*Disclaimer: I have never actually performed this reaction and I could be dead wrong.