What does it mean?
Private Buddha. One who, like a Buddha, has gained Awakening without the benefit of a teacher, but who lacks the requisite store of pāramīs to teach others the practice that leads to Awakening. On attaining the goal, a paccekabuddha lives a solitary life.
-from Access to Insight
Why does it matter?
In each cycle of the world, there is one Buddha. He achieves nibbana by himself, then teachers others. Some of his followers can also achieve nibbana and are called arahats. They are just as enlightened as the Buddha, but have a different name since they achieved their enlightenment with the help of a Buddha.
But there is also a third class of enlightened beings, the paccekabuddha. Like arahats, paccekabuddhas are just as enlightened as the Buddha, and like the Buddha, they did it themselves without a teacher. But unlike the Buddha, they (for whatever reason) don’t go on to teach, form a school, gather disciples, and so on.
I find it to be a beautiful idea that right now there might be a paccekabuddha somewhere in the outback of Australia, blissfully living out his years a fully enlightened being having never heard of the Buddha. What if the kindly old woman living alone with her cats down the street is actually a paccekabuddha?
There is an interesting little sutta here about the paccekabuddha.