Mucho is literally "much." In the context of "mucho gusto" it doesn't really translate directly. The closest English approximation would be "really glad" or "my pleasure" or "much pleasure."

It is an adjective used where we might normally put an adverb.

"Muy" is the corresponding adverb. For example, where we say "very well" or "really well," Spanish speakers would say "muy bien."

During my first year in Venezuela, I commonly made the mistake of calling good things "mucho bueno." This remains a source of amusement (and an in-joke) among my friends there to this day.