My father worked in fuel procurement for a few airlines. He hated fuel price instability as much as you hate air fare instability.
In a nutshell: An airplane cabin is segmented into a number of classes. There can be a dozen, or even more classes, even though you only see economy, business and maybe first.
Each class gets allocated a number of seats and the actual booking class can have more, or less restrictions attached to it (for example: refunding, or changing the ticket, mandatory Saturday night stay, minimum duration of stay, etc).
The more flexibility you require the more expensive the ticket becomes.
Even though it looks very confusing from a passenger perspective and prices can fluctuate on an hourly basis, depending on the number of seats available for a specific sub class, the concept makes a lot of sense from an airline's perspective.
Stable prices means that consumers and airlines can both plan better.
For consumers, it means confidence in buying a ticket.
For airlines, it means predictable revenue, and costs, which should add to the market cap of the companies.