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:
A structure that needs resources raises a construction site instead of appearing right away. See Resources for how a site gathers what it needs.
A structure the occupying faction wrecks is not lost. It leaves a ruin in the same place. You can repair it for a share of its build price, and anything stored inside survives. See Ruins and Repair.
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. Once the occupying faction holds enough in reserve, it can pick a town or base you hold and start a slow campaign to take it back. The campaign runs in stages: harassment, then a forward base, then a siege. See Counter Attacks for how that plays out. 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.
A base's own defence is only one of the forces the occupying faction keeps in the field between battles. See Patrols and Garrisons for how those forces hold ground, keep their losses, and grow as a campaign goes on.