"There were days—there were many days—these words could burn stars... and raise up empires... and topple gods." -- The Eleventh Doctor, in The Time of Angels, discussing the powers of Old High Gallifreyan
Gallifrey was the planet that was home to the Time Lords, the most powerful, advanced race in the galaxy, possibly the universe. Not every resident of Gallifrey was a Time Lord, but all the Time Lords were Gallifreyans, albeit ones who had undergone a rigorous initiation of some sort.
The existence of Gallifrey was not shown until several years into Doctor Who, and was not named until some years later. During the run of The Fourth Doctor through The Seventh Doctor, some action took place on Gallifrey, and the culture and politics of the planet took a place both in the television show and in the spin-off media.
The continuity of Doctor Who is large and complex, and the location, history and role of Gallifrey has been viewed many ways. I am not an expert on the history of Doctor Who, but Gallifrey in general was seen as a glorious, powerful society that was in general humane enough, but also was prone to arrogance and stagnation. It was to escape the confines of Time Lord society that The Doctor stole his TARDIS and went rogue, although he always maintained a love/hate relationship with Gallifrey and its culture.
The most important event in the history of Gallifrey, at least during Classic Who, was the invention of time travel, by the Gallifreyan culture heroes Rassilon and Omega. This gave the Time Lords the power to secure their planet, and to explore the galaxy, although they were never empire builders.
Between the classic series and the revival series, Gallifrey was destroyed, in a war between the Time Lords and their arch-enemies, the Daleks. This war was called The Last Great Time War, and apparently was intense, violent and convoluted enough to defy all description. It was not shown, except for passing. All that we learn is that The Doctor destroyed Gallifrey and the Daleks, in an attempt to avoid universal destruction. This left The Doctor as the last of his race, wracked with guilt at destroying a planet that he continued to describe as a beautiful place full of the universe's most advanced culture, and a megalomaniac society bent on universal control.
Although the long reach of the show (and affiliated media) gave many opportunities for Gallifrey to be portrayed, it was rarely in the spotlight. One of the constant themes of the show has been how much The Doctor prefers the company of the most mundane of earth residents. Many viewers of the show would also rather watch a show that focuses on situations that they are familiar with, rather than the political intricacies of an incredibly complex society. For that reason, Gallifrey, whether existing or destroyed, is usually used as background and to evoke the idea of unearthly, mysterious power, rather than being described and used as a mundane setting.