There's a lot of variables that go into pricing a flight, both in terms of the cost of the flight to the airline company and the value they think they can get for it. Obviously, if you're booking far ahead on an empty flight they have a lot of seats left so the supply is high and the demand so far is low. If you're booking the day before the flight leaves and there's three seats left and it happens to be going to a popular desitnation then the airline figures it can charge more and often can, conversely, if it's only minutes before the flight leaves they sell the seats cheap because its better to get half of what you normally would for the seat than nothing.

Add to this the fluctuations in the price of fuel and what people are willing to pay during peak buying times and you've got a constantly fluctuating price.

tl;dr black magic.

edit: you asked about peak buying times. I don't know what it is but whenever I've shopped for a flight around 11pm-midnight on a Sunday it seems to be a low traffic time for most booking sites since I'm guessing the majority of bookings happen during work hours so the flight prices seem to be a bit cheaper then.