In Heroes of the Storm you have a CORE that you must protect and the enemy team has their own core that you must destroy.
Objectives - These are different per map, but typically they can push Lanes or Forts very quickly and shouldn't go ignored unless your team has some strategy to count the advantage gained from having completed the map objectives that will appear.
LANES - Destroying forts upgrades minions in that lane. They are the default MOBA style gameplay and you can gain experience by sitting in a lane when your own minions kill other minions.
Mercenary Camps & Bosses - These can vary in each map, however once you are able to capture a camp by defeating it and capturing it.. you will be able to use those Mercs/Boss to give you an advantage to push against the enemy team.__________________________
Heroes are split into different categories for their particular role in fights.
Tanks & Bruisers absorb damage and often use crowd control abilities to delay or initiate a team fight against the enemy team.
Healers help sustain a team and allow them to fight for longer without having to return to base leaving the team without exp farming on a lane.
Support have uniquie abilities such as shielding team members or unique lane abilities for gathering experience for the team.
Melee Assassins do huge damage in close combat but could be weak when attacked at range.
Ranged Assassins are the common damage dealers and they all have their own strengths and weaknesses to other assassins.