I have been asked this question many times and the best way for me to describe it is, it is your business identity. It is not a banner, although it can be used in a banner, your logo is something that makes your business instantly recognizable. Think of some of the 'big' companies out there like Microsoft, Coke, Nike, etc. Whe you see their logo, you automatically know the maker. A logo does not have to contain graphics to be recognizable either. Many big companies go with a simple text logo with unique fonts or standard fonts with small additions as their logo.
Once you have your logo you can now use it on a wide variety of applications but be careful. Images with a lot of gradient colors do not print well so while they may look flashy on the web, they won't look so great in print. If you are planning to use your logo on more than one medium be sure to have your designer make the logo in grayscale or black and white as well as a color version. This will help ensure that your logo will look just as good in print and it will give you a less expensive option for printing if you want to add it to tags, business cards, letterhead, etc.
Be sure to stay tuned for more tips and tricks on how having a unique business identity can help with branding and how you can use your logo to help promote your business.