Miltary Bases are located around the map (in Everon there are 6). At the start of the game these will be occupied by the OF and resources will be allocated to them on a regular basis to add/replace soldiers/assets or build upgrades.
You capture a base by approaching the flag there and using the capture action on it. That starts a QRF: the occupying faction sends reserve forces in from every other base it still holds, and the base only changes hands once the battle has been won.
Only one battle runs anywhere on the map at a time, so while another capture (or a counter attack) is in progress the action is not offered.
When you own a base it gives you certain advantages:
Taking a base also raises the pressure on the occupying faction across the whole campaign, and losing one takes that pressure off again. See Threat.
Nothing you take is held for good. The occupying faction spends its reserves on the bases it still has, and when it has more than it needs it will pick a base the resistance took and come back for it with its own QRF, then wait a while before trying again. A base can change hands several times over a campaign.
Camps and FOBs are also known to the occupying faction, which sends troops out towards them when it has soldiers to spare.