Mission running is PvE content: getting missions from NPC agents and then completing them for the mission rewards and the bounties from any hostile NPCs you destroy along the way.
If you decide to pursue mission running as a source of income, you’ll want to build up standing with a particular NPC corporation in order to get access to higher tiers of mission agents (which can then give you harder missions with better rewards).
In order to tackle these harder missions you’ll also want to continue upgrading to larger classes of ships such as cruisers and battlecruisers. In general, you’ll want:
The only battlecruiser that alpha clones can use is the Gnosis.
You can read more on the UniWiki ‘Missions’ page.
Once you’ve received a mission from an agent, you can look it up in the EVE-Survival mission listings to get more details about what kind of dps you might face from enemies in the mission and which enemise may trigger more spawns.
Mission running produces a fairly steady stream of ISK - the mission rewards will pay out a certain amount, plus you’ll also be paid the bounties for any hostile NPCs you killed.
You’ll also be rewarded with loyalty points (LP) for the NPC corporation that is giving you the missions. These LP can be traded for items from the NPC corp’s Loyalty Point Store.