The Ancients are an old people, having lived in mass population thousands of years ago. They would come, "settle" the Planet, and move on. In essence, they were the Planet's medicine. So we have all come to ask as to why they are all gone now. For a more in-depth explanation of the Ancients' behaviour and physical characteristics, please see the Biological characteristics of the Ancients record.
Initially, several stories arised from the desire to discover the Ancients' origin. One popular story states the Planet begged for them in crisis, and from its tears borne the Ancients. Another well-known story tells of how, when the Planet was created, they emitted from Lifestream. An infamously notorious story explains that this Planet is not the only planet upon which the Ancients inhabit, settle, and leave. Whatever the truth may have been, they were here for thousands of years before.
3000 years ago, a "calamity from the skies" fell to the Planet, and upstarted the Ancients. This was Jenova, and her dormant presence upset the Ancients. In addition, she left a huge hole in the Planet near the Icicle area. It was reported to be several miles deep, revealing much of the insides of the Planet.
To the Ancients, this was a terrible occurrence. They believed the crater to be a gargantuan wound in the Planet, which the responsibility of helping to heal it was theirs. And this they did, for thousands of years. After doing carbon tests and other such forensic sciences, it was discovered that the wound was much larger and deeper at first. The Ancients, though skilled in their healing, were no match against the huge wound Jenova had created.
But only 1000 years ago did the Ancients suddenly begin to die out. Many people thought that they were "moving on". But a discovery of old records tells us that wasn't the truth. According to one of the last surviving Ancients in an interview with the late Professor Gast, a terrible disease was introduced to the Ancients by Jenova, herself. It was apparent, at this point in time, that Jenova's intent was highly malicious, and that with her still there, the Planet could not heal. And it seemed as though only Ancients could rid the Planet of Jenova.
But as it so happened, all the Ancients were finally destroyed. The earlier ones by Jenova's disease, Geostigma, the second one from fatigue, and the very last Ancient was killed by Sephiroth. The Ancients, although gone, played an essential role in the Planet's future. Without them, it may seem dire.