Definition
The principle of indifference says that when you have no reason to regard one possibility as more likely than another, you should assign them equal probability. If a die has six faces and nothing favours any face, each gets probability one-sixth.
The principle is attractive because it seems to derive numerical probabilities out of pure ignorance — it tells you what to believe when you know nothing relevant. It is the classical route from a symmetric situation to a precise figure, and it underlies the textbook treatment of coins, cards, and dice.
Why it matters
How it works
The trouble is that "no reason to prefer one possibility" is not well defined until the possibilities are fixed, and they can be fixed in incompatible ways. Priest gives the case of a factory producing cubes with side length between 0 and 1 metre. Apply indifference to the side length and you get one probability that a cube is smaller than a given size; apply it to the volume instead and you get a different probability for exactly the same physical fact.
Both descriptions are legitimate, yet they disagree, so the principle alone cannot say which is right. This is closely related to the reference class problem: in both cases probability turns out to depend on a prior choice the principle was supposed to make for us.