A lot of players in EVE Online spend a large amount of time running missions. Missions are PvE content which is instanced. Now somebody is going to protest that there are no instance portals in EVE, but for all practical purposes missions are instances, that is only you and people you invite can reach them. Another player who by chance has the same quest in the same solar system will come out in a different instance, and not turn up in yours. Now there are 4 different types of missions, but mining and trading missions are very rare, so in over 95% of cases your mission will either be transporting something from A to B, or going somewhere and killing NPC ships. You can influence what type you get by what kind of agent you talk to. But the actual mission you get is a random one, out of a list of over 400 different ones.
Missions are rewarded with three things: ISK (money), standing (a reputation score with the faction you work for), and loyalty points, which can be used to buy things in a special loyalty points shop. How much you get depends on what agent gave you the mission, there are 4 levels of agents, and each agent has a quality from -20 to +20. The higher your standing with the faction, the better agents you get access to, and the more rewards you get.
Nevertheless there is a trap for new players, the difficulty of missions goes up enormously from level I to level II. While the level I missions were rather a bit too easy for me flying in my destroyer, my first level II mission Damsel in Distress turned out not so well. I warped in and was immediately surrounded by 8 frigates and a cruiser, all in range to shoot at me. I thought that if I could take out the cruiser I could warp out, repair, then come back for the easier enemies. What I didn't know was that killing the cruiser would spawn 10 more frigates, elite ones, and before I could warp out I was pulverized. I tried with a cruiser to recover the stuff from my wreck, but was forced to flee before losing that one as well. I'd need a better ship, which in EVE means waiting for the skills, to reliably do level II missions. Of course some people do them in smaller ships, but using much higher skills in everything relevant and tech 2 modules.
The annoying thing is that I did the missions for the standing, and the standing only increases at snail pace from level I missions, even with the relevant social and connections skills. I would need a standing of 8.00 to enable the use of jump clones (hearth stones), but each level I mission only raises my standing by 0.01 or 0.02. In fact I lost several missions worth of standing for not being able to complete that level II mission. So right now I'd either have to grind a huge lot of level I missions (and I'll certainly do some to learn to fly my new cruiser), or I'll need to wait for the skills for a bigger ship and do level II missions. Or I could join a group from my corp, but they usually do level IV missions, and I would be just leeching.
In summary, missions in EVE are where the game most closely resembles classic MMORPGs with quests. And curiously enough the instanced nature of the combat mission targets makes the missions feel more like a single-player game than doing quests in World of Warcraft in an open world where you might see other players on the same quest killing the same quest mobs.