Turn off the computer. Well, not right now, as you're reading this! and ponder how people find your businesses. There are two ways, one has been traditionally called "word of mouth" and the other is paid advertising. And if you just replace "organic" with "word of mouth" you have a pretty good idea of what it all means, and if your business is missing the most important part of your marketing mix.
Organic, whether on the web or "In Real Life" (as if the web isn't real life!) is all of the things that you do to call attention to your business aside from paid advertising. It's people talking about your business. It's recommendations because you have done a good job. It's an article in a magazine, the newspaper, or nowadays in a blog. It's what the publicity people in marketing call "the buzz", or the chatter.
So, long before you sign up to pay for advertising, you should be everything organic that you can. And you would be surprised at how many businesses fail to do this, both "In Real Life" and on the web.
The good news is that organic promotion is free. The bad news is that it's a lot of work. But it's part of being successful in business, and it always has been. If you don't have time for this, there are a lot of people who will be happy to charge you for "shortcuts to success". No, it's not that I don't trust them, it's just that you really don't need them until you have done as much organic stuff as possible.
I have been promoting my business organically for over a decade now, and I'm still seeing things that I need to do, and new stuff is being invented all of the time, like Google+. So start with a strong presence on Google. Get a Google+ profile and a Google+ business page. Set up Google Analytics. Write about your business in a Google blog. All of this stuff is free, and organic is the best advertising you never paid for!