Multiplayer in Dark Souls III is unusual and structured differently than most online games. You can choose to play offline (and if invasions really bother you, this is one way to skip them), but if you are connected, you are always online… if not necessarily walking around in the world with other players constantly.
Instead, Dark Souls III uses a system where you can interact with other players by leaving messages on the ground and joining or being joined by other players (sometimes forcibly!).
Note that even if you do play offline, there are still some messages (and AI invaders) placed by the developers to help you out in a few spots and give you trouble in others.
It's important to note that Dark Souls servers are platform-specific. You cannot play with friends on your PlayStation 4 if they're playing the PC version of the game. You can play with people in other regions, though, as long as you have a strong connection.