When you look at a PCB, you see a bunch of printed circuits. There are layers of circuits built into the board. In general... The more layers, the more circuits can be built on the same size board. More importantly, this means that the same number of circuits can have more space/insulation in between, reducing cross-talk, electromigration, etc.
Are all "higher layer" PCB's inherantly more stable... Not necessarily, of course. There are many, many other factors at work, also.
Obviously a higher amount of layers generally means a higher cost of production. That's the only downside.