Defending the Crystal Core(s) is the main objective in order to complete any map. If any Main Core gets destroyed the map will fail.
The Amount of HP a Core has depends on difficulty and map.
Sub Objectives
Sub Objectives are a secondary type of "core" to protect. If the Sub Objective gets destroyed the map won't fail but a new lane often opens on the next wave. If you lose the Sub Objective on the last wave it can be ignored.
The Amount of HP a Sub Objective has depends on difficulty and map.