There four different objective on every map. Every one gives you unique bonuses. To capture an objective, fly into the green ring surrounding it and wait until the green bar is full. To decapture an enemy objective, fly into the ring surrounding it and wait until the red bar is empty. You can lock an objective for 30 seconds by pressing the 'G' key. This way the enemy can no longer capture the objective. This can only be done once every two minutes.
The planet gives your team one additional command point per second. You can get more cp via the use of the advanced colonization upgrade. Planets are a high priority objective, as the loss of the extra CP will deprive your team of many upgrades. Get it as early as possible to start generating CP, and protect it! If the planet will be taken over, try to lock it before you leave to maximize uptime. The CP spent is outweighed by the CP saved for the rest of the team.
Anomaly (aka Techlab)Edit
The anomaly, commonly also referred to as 'techlab' or 'tech' allows your team to get new techlevels faster, which unlock higher levels of upgrades and skill levels. Each tech lab launches an armageddon missile at at Techlevel 21 and every level after. The tech lab is arguably more important than the planet or the wormhole, since it controls both tech level and the armageddon missile for breaking stalemates. If a tech lab is taken over, try to lock it when retreating to maximize the uptime.
Wormhole (aka Portal)Edit
Wormholes allow the team that controls them to jump between them and the base. Simply fly into its ring, and click on the green icons on the minimap. This costs 50 CP. You can also hit the 'R' key to jump back to home base. You can also upgrade your ship at wormholes. If your team has the convoy upgrade, convoy ships are spawned from portals and make their way to your shipyard.
This objective can be absolutely paramount to obtain, since it is often placed at the midway point of a map, cutting travel time and creating a buffer-zone between the enemy and your base that can be teleported to. It isn't usually important to capture it first, but to obtain it after a battle so that dead players can return to help hold the line.
Crystals give your minions a hitpoint-bonus. This can be upgraded via the advanced refinery-upgrade. This is the least important objective, and should be ignored in favor of chances to attack a planet, techlab, or wormhole, or to destroy base turrets.