Wars are events that can be accessed when you join a corporation.
Each player are given 10 bases. The difficulty is decided by starport capacity. It also seems to depend a bit on HQ level. Right now I am hq 5 and my heroes actually take damage when invading while as hq 4, a single squad of marines could take over each base.
Wars can be started by a corporation's president or by their top managers. However, just because a war is started doesn't mean you will make it there. To qualify, a corporation must score 1000% destruction in 8 hours, as much as the full potential of a single person. The corporation's top 20's results will count for the war. The winning corporation's members can open crates they earned by destroying bases. 20% for a base nets you a bronze crate. 40% gives you silver, and 60% gives you gold. Each crate contains medals, modules, or antimatter. So far, from my experience, if you get all 10 bases, then you get 5 crates with medals, 4 with antimatter, and 1 with modules. Specifics about crate rewards are stated below:
Bronze: 15 medals, 25 antimatter, or a common module
Silver: 30 medals, 50 antimatter, or a rare module
Gold: 60 medals, 100 antimatter, or a legendary module
Do not upgrade your starports if you can't get 1000 percent in war with heroes or mercenaries. Always prioritize heroes first.