MMORPGs are basically multiplayer games aim at groups of players. The content in MMORPGs are therefore usually designed to encourage you to play with or against others, to have fun (though not always). However, many MMOs today start to offer solo content/single-player mode with nice storylines.
So that you can do quests completely alone or play certain dungeons by yourself. You'll be traveling alone, solving problems without others' help. There are some reasons to have a single-player/offline mode in MMOs.
Firstly, some players don't have so much time but want to level up as fast as posible. Sometimes its not fun to be in guilds which have many rules and requirements. The possiblity to play a lone wolf to play a big chunk of the game content helps to keep this type of players in the game. For the developers, solo content gives them an opportunity to design different experience, say, stories, mechanics, and more.
Secondly, the solo content can somehow help players transit to group content smoothly. And they may keep playing the game longer than they would. It might be strange that solo players play a multiplayer game's offline mode. The point is the mode offers different freedom and features and ways to have fun in an MMO.