A plane has a fixed number of seats on board. The first seats sold for the flight are offered at a lower price, which increases if the flight begins to fill up quickly or as the date of the flight gets closer. The idea behind this is that business bookings are normally made at the last minute by companies with deeper pockets than vacationers, who book their tickets long in advance.
If one airline on a particular route drops its prices, then other airlines flying the same route are likely to drop their prices to match that fare. This generally only applies to flight routes that are in high demand.
Each travel class has a number of fare classifications, such as an Economy "Flex-Saver" ticket, or Economy "Fully-Flex" tickets. The cheaper fares generally have more restrictions on what the passenger gets in terms of changes, cancellations and upgrade allowances. This can create large price fluctuations in the same class based on the number and types of tickets being purchased.