How successful you are with an online business will depend on how hard you are willing to work on your business especially in the early days. Your knowledge and skill will also be important but just like in the bricks and mortar world those businesses that succeed are those who find a niche market and can make a profit from selling their wares.
An online business could be anything from selling homemade greeting cards, selling secondhand goods on ebay, doing research for people, web design, giving advice and is really limited by your own skills, time and experience.
It is well worth doing some research on the demand for your products by looking at what your competitors are selling and whether you can compete with them. Further useful information is available from Business Link.