What do you get from playing online?
Dark Souls (and Demon's Souls, though it's not for PC) are completely unique in how the multiplayer experience is seamlessly interwoven with the single player game. Other players helping and hindering you, directly and indirectly, is a concept the entire game is designed around.
Certain entire aspects of the game won't "work" as intended if you're offline. BlackFlyme mentioned "covenants", which are factions you can join that mostly let you interact with other people's games in different unique ways, be it PVP (consentual or not) or co-op. Certain actions in the game are "punished" by being attacked by player members of a certain covenant, for example. The covenants and what they do are all tied directly into the game's lore and backstory. The game's still entirely beatable offline, but you miss out on a lot of things that were intended to be a part of the core experience.
A specific example from Demon's Souls (Dark Souls' predecessor) was that there was a major boss in the game that was actually another player summoned from their game to fight you. If they succeeded in killing you, they'd get a unique item for it, but you had to defeat an actual human being to progress through the game. Playing offline would get you a (usually much easier) NPC boss in their place.