Jefferson wanted people to be able to choose a path and work toward it without interference. People had the right to be left alone. You could choose your happiness without the government or anyone else interfering. At its foundation, this is the American Dream.
One thing that should be noted is that Jeffersonian democracy was quite different from our concept of what democracy means. First, as others have noted, neither he nor really any of his contemporaries seriously contemplated equal political rights for women, African-Americans, or (for the most part) Native Americans. But Jeffersonian democrats also held a conviction that seems contradictory to our modern politics: they argued that political equality had to be undergirded by a rough economic and social equality. This was an important aspect of what we have come to know as republicanism, which is perhaps a better way of describing Jefferson's thought than "democratic" as we understand the word today. While they valued property rights, they also were concerned that the amassing of great wealth which seemed to be inherent to a society that placed such an emphasis on property had a corrosive and corrupting effect on the body politic.
In fact, Jefferson's thought, and those of the Jeffersonian Republicans in general, represents for some scholars a turning point between this classical republicanism and a new liberal ethos that tended to view property rights, the free market, and limited government intervention as more important to political liberty than economic equality. Other aspects of Jefferson's thought that were very important and very much in the democratic tradition include a commitment to such civil liberties as a free press and religious freedom. Overall, we tend to view aspects of Jefferson's thought as contradictory and even hypocritical, and while this is a fair charge in many cases, we should also remember that he and his contemporaries would not have necessarily understood them as contradictory.
Jefferson defined democracy in two ways in the Declaration of Independence. First, he defined it as a system in which the government ruled by the consent of the governed. Second, he defined it as a system in which the government exists to protect the people's rights. In practical terms, this means two things. First, the people get to vote. They get to choose who will govern them. Second, those whom they choose to govern cannot simply do whatever they want. A democracy must have a limited government that cannot infringe on the rights of the people unnecessarily.
Of course, Jefferson's idea of democracy did not include the right to consent for women or non-whites. It did not include the idea that their rights had to be protected.
Jefferson was the champion of agrarian interests and the idea that the power in a democracy resided with the common people of the republic. He opposed the idea that elitists should run the government and that the government should adopt forms and policies similar to the aristocracy of England.