Heaven's Garden is the centre of Heaven. As it names implies, God ruled Heaven from it.
Different individuals see "Mission Control", as Zachariah called it, differently. Angels presumably see it as God's Throne Room, while to others, it's Eden, and to Dean and Sam, it's the Cleveland botanical gardens where they went on a class trip. The gardener's name is Joshua.
When Sam and Dean are shot and sent to Heaven, Castiel contacts Dean, telling him to find Joshua, as he talks to God, apparently. As communication with God would undoubtedly be helpful, they went in search of the Garden. One sees what they desire in The Garden according to Joshua; the boys see it as Cleveland Botanical Garden, where they went on a school trip.
Zachariah was in charge of the garden and had higher authority than Joshua, as Joshua stated that Zachariah could fire him.