A heavy cruiser was a Capital ship. Following the Anaxes War College System of starship classification, heavy cruisers were medium sized starships at a size of roughly 600 - 1000 meters. They were much larger than Corvettes or Frigates but smaller than ships of the Star Destroyer or Dreadnaught classification.
Long before the Clone Wars, heavy cruisers were among the largest starships of the Galaxy. But that changed, when the Clone Wars and the Rise of the Empire forced a radical mobilization and militarization throughout the whole galaxy and larger, more powerful ships, like the Star Destroyers, were constructed.
Heavy cruisers were often the backbone of any fighting fleet as they fulfill many important roles. Such roles included planetary bombardment, troop transport and ship to ship combat.
However, most heavy cruisers were not equipped with starfighters. Therefore, they were in need of smaller support craft like frigates, corvettes and carriers, taking starfighters into battle.