It isn't necessary to be a part of a writing group. Plenty of writers have done just fine without 'em, and I've heard some decry such groups as wastes of time at best, and killers of creativity at worst. And that can be true.
But it doesn't have to be that way. A good writing group can inspire you. It can prop you up when you want nothing more than to bang your head against a wall, and push you to become better than you might have been going at it all by your lonesome. At it's best, a good writing group challenges you to push the envelope of what is comfortable, and helps you discover what you are capable of, even while gently advising you that your magnum opus needs a teensy-weensy bit more work before you bring the world to its knees with the power of your prose.
MY writing group is helpful, for two reasons: one, each person in my group is a serious writer. And by serious, I mean no one here got bored at work and decided that they would pick up a pen (or laptop, or whatever) and just start writing. Not that there is anything wrong with that. I applaud anyone who wants to take up the art. But there is a difference between someone who is writing for fun, and someone who lives to write. Read, oh, The Grapes of Wrath, say, and then go and read some of the fodder in many of the 'literary' magazines out there, and you'll see what I mean.
Serious writers are continually learning, and are always open to anything than can help improve their writing. Writing is difficult work(despite the adage that anyone who can speak can write) but it is a labor of love, and there is nothing a true writer would rather do. So we study, and practice, and do all that we can to be the best writers that we can be. And that is a key requirement in a good critique group. You want the people in your group to be able to tell you more than "Hey, that's pretty good," or "Sorry, I didn't like it." You want them to be able to tell you what makes the story "pretty good," or why he or she didn't like it. If they can't do that, then what have you learned?
One other thing that I find helpful about my writing group is that most of us write in different genres. That may sound counter-intuitive: as a horror writer, why wouldn't I find a group of other horror writers to be in? I can't really answer that, because I have never been in a dedicated horror group. It may be amaze-balls, and I can certainly see how that could be good for me. But having writers in other genres critiquing my work has helped me, by forcing me to think outside of the usual conventions of my genre. Sometimes, a person who writes and reads something other than horror is able to help me look at my work in a totally different light, enabling me to bring more depth to the piece, and that is always a good thing.
What it boils down to, for me, is that if you're a new writer, wanting to get serious, you don't have to join a writing group. If you want to write badly enough, you'll find a way to do it - alone, or with others. But if you do decide to join a group, make sure that you find one that is made up of like-minded writers who are knowledgeable and work hard at perfecting their craft. A writing group with serious writers can help you become a better writer by giving you honest and fair critiques of your work.
Now, go. Be writers.