That definition has been a moving target for me - and I'm going into my sixth year. I don't doubt it will continue changing. I would probably give any Harvard Business School grad a case of hives.
My first year, the business was successful if I managed to get 60% signups that were not people that I directly knew - in other words, not friends or family. While most of my signups were friends and friends of friends, I did get several clients through freelance hosting and design work, a few through forum posts, and one bit of word-of-mouth advertising.
My second year, the business was successful if I was able to get a certain profit margin. In all fairness, it wasn't a huge profit margin - but I got it.
My third year, the business was successful if I managed to move to my own servers and maintain a certain profit margin. I didn't quite make the profit margin that year; but I did move to my own server. I was also able to better tailor my plan specs and increase features without raising prices - in part, because of the move to my own server.
My fourth year, I was fairly modest in defining "successful" - it was a bad year, extra stress on me, my support team was in flux, and I just wanted to maintain service levels and not go into the red.
My fifth year I was going to pour on the guns in terms of advertising and marketing, especially since I had stayed pretty low-key in years one through five. I figured that after surviving five years, I could safely say that I was in this for the long haul and that I had been around for a while. The plan to amp up the advertising kind of fell apart...but that was completely my fault. (Well, that and the relocation.) I have that same goal this year, and am actually following through.
In overall terms, I want the business to grow to the point where it can support me and pay a decent wage to my staff. I want to have the ability to keep learning about server management, fine-tuning my knowledge of what my clients might need, and figuring out how to provide that safely and reliably. Essentially, this business is my retirement plan: it will give me some income so that I don't have to try and live off of Social Security; and it will give me something to do so that I don't go batty with boredom. (Now I just have to keep the business active for another...oh...25 years, and I can see how well it meets that particular goal.)