The following is not intended as a comprehensive answer addressing the fare policies of all American domestic carriers. It does, however, provide a pretty good summation of the general policies prevelant among most major carriers.
Airlines know in advance how many seats are going from one city to another any given day. They also have a pretty good estimation as to how many travellers will fill those seats, and how far in advance said travellers will buy the tickets for the travel. Based on this information, the airline will designate a certain number of seats on every flight as carrying a lower than full fare price. There are often several lower than full fares available, and for each there will be a specific number of seats available on the flight.
As the flight’s seats are sold, those seats are removed from the available seats. If, for instance, there are 50 seats available at the $200 round trip price, and someone buys 5 of them, there are now only 45 seats at that price. If there are only 4 left, and you want to buy 5, you will be out of luck, unless you are willing to pay a higher price for one of the seats.
When you look up the availability of seats on a flight through a booking service, you see all available fares with seats still available on the flight. Obviously, it makes little sense to book a seat on a flight at the full fare four months in advance, but the number of seats at a minimum that will be sold at full fare is already set. So they show up as available from the moment the flight is made available for ticketing.
As time goes by, and the date of the flight gets closer, certain fares become unavailable. Any unsold seats at that fare are kicked into a new designation (often the full-fare designation, rather than the next most expensive fare). Eventually, you reach a point where the only seats available on a flight are full-fare seats.
Sometimes, as people who use priceline.com know, the airlines will let other services have tickets at reduced fares to resell despite the fact the normal restriction on advance purchase is unable to be met. For instance, a carrieer might have a fare that is 75% off the full fare, but which has to be purchased 2 weeks in advance. Now, it is only 13 days in advance, but there were 10 unsold seats at that fare. The airline, if it anticipates it won’t be able to sell those seats at a higher fare, may allow another service to market the reduced fare, or may have some other mechanism for filling those seats at less than full fare.
This also is how most airlines now handle ‘bereavement’ fares. If there are unsold seats that were originally designated at reduced fare, the airline will waive the advance purchase requirement. In 1993, my grandfather’s death caused me to fly on very short notice (one day) from San Jose to Chicago; because of timing constraints, no airline had a reduced fare left on flights that would work; as a result I ended up flying for full frieght, which even back then was around $1600 round trip. And, in one of those lovely examples of modern business, typically the reduced fare they will try to sell you in such cases will be the MOST expensive unsold reduced fare, not the least expensive. Only if you sound like you can’t go at that price will they ante up the possibility of a lesser cost…
Ticketing agents and/or industry personnel with more accurate explanations are invited to help out here. 
