In my case, I've been using Twitter on a very regular basis loooong before I even considered making a comic--I used to be in another online art community that had a BOOMING Twitter population, and it was primarily used not only as a way to share the work you were doing, but also to meet and talk with other people in the community and make friends and just have a good time overall. Back then, we used to use Twitter almost like a chatroom--we wouldn't use the @ mentions, we'd tweet hundreds of times a day--and it was a lot of fun! I met a lot of my closest friends that way that I'm still close to even now.
In the webcomic community, I've more or less had the same experience--a LOT less tweeting, but to be fair I'm nearly 10 years older than I was when I first started Twitter and therefore a lot more busy, haha! But for me, I don't really view it predominantly as a place to promote my art or whatever--I DO post my art and comic and all that to my Twitter, but I also use it just as a way to talk with other people about things that I like, whether it's comics, music, animation, etc.--or to be a part of largescale conversations about issues or topics I'm passionate about.
I really think Twitter is best enjoyed as a social platform as opposed to a "post my art and run" type platform you see a lot on Tumblr or dA or other such sites. I've definitely met a lot of really cool people in the webcomic community through Twitter who I now consider very close friends!