Dragonlords were the rulers of the Valyrian Freehold that rode and controlled dragons. They played a large role in the Valyrians' defeat of the Ghiscari Empire to the east and the Rhoynar people to the north, vastly expanding the size and power of the Freehold.
In the books
In the A Song of Ice and Fire novels, "dragonlord" was a title reserved for members of the forty noble families that vied to actually rule the Valyrian Freehold. They were called dragonlords because they could ride and control dragons using whips, horns and sorcery. It had long been the custom of the dragonlords of Valyria to wed brother to sister to keep their bloodlines pure, and they were said to be strikingly (some say inhumanly) beautiful.
Throughout the history of the Freehold, the number of dragonlords no doubt fluctuated depending on circumstances. During Valyria's wars against the Rhoynar over a thousand years ago, there were at least three hundred dragon riders, the number sent against the army of Prince Garin (who was soundly defeated).
The Targaryens were a minor dragonlord family, far from the most powerful, but are the only family that survived the Doom of Valyria with dragons. Thus members of House Targaryen are known as dragonlords in Westeros, even after the death of all the dragons.