Incursions are based on large masses of monsters that roam the wastelands.
You can pair up with a few other explorers from your corporation and take out a pack of monsters.
If you're good enough, you can also earn exclusive rewards.
Here are some important points to consider:
All players in an incursion kill as many monsters as they can before they die without multikill buffs or limits.
There are 20 total reward tiers per incursion.
Every 24 hours (at 00:00 server time) you get 1 incursion run. You can have a max of 3 incursion runs.
Incursion groups are corporation-specific, meaning you can only join groups with other members of your corporation.
Incursion logs are sent to both your personal log as well as the corp log, so you can see what other corp members are doing.