A lot of people have different opinions on how this happens. Some are in their stage of experience in blogging that they are new and others have been writing for years. However, there are some elements like Onibalusi Bamidele writes in his article What are the Elements of Successful Bloggers? that do help make the difference between a normal everyday blogger and successful blogger.
A successful blogger is one that can influence people. (By the way, Micah Baldwin has a great article and slideshow on his article A Community of Influence that defines influence, how it is measured, and much more.) It does not matter how many people it is. If you can influence one person, you have succeeded. How you reach many people depends on your own goals – whether you are going to try to reach out to a target audience and how much time you want to invest.
You have to be knowledgeable about your topic. An author cannot convey a convincing story if they do not know what they are writing about.
You have to like what you are talking about – be passionate. You could like just about anything, but pick the one that you know you could talk about and connect with others. This topic is one you could pick apart and creatively share with others in a way that they are encouraged to add their own ideas or might adopt yours.
Authenticity. Liz Strauss writes about this in her article What Makes a Blog Compelling? – She is right. (And by the way, she is extremely successful. I hope to have the privilege of meeting her again in person soon.) People can figure out fast what a person is like, so you have to be yourself.
Encourage conversation, and be active. You might see a post on another site that you thought did not quite cover everything you wished it did. Of course, you could leave a comment, but why not blog about it and leave link back to the original article if you have a lot of interest in the topic. Not only are you creating content, but you are carrying on a conversation. Make sure to be involved in that conversation and not make it look like you were just trying to pimp links into your site.
To you, what makes a successful blogger?