Trying to expand my knowledge of Magic, and hopefully become a better player, I've come across several references to "layers." From what I've been able to find, they are as follows:
Could someone elucidate the significance of the order and exactly what this layering thing means?
I completely agree with Hackworth that an in-depth answer would probably require an article, but I don't recommend the Comprehensive Rules (very dry)... so try this article instead.
It's got loads of good examples that really demonstrate when this stuff becomes useful. e.g. You have a Giant Growthed Grizzly Bears (2/2 +3/+3 = 5/5) and someone casts Ovinize on it (loses all abilities and becomes a 0/1). Without reference to the layers system, how do you explain to someone that the Bears are now 3/4 creatures, not 0/1?
The basic answer is that the layer system determines how to apply continuous effects to every object in the game so that they get their actual state beyond what's printed on the actual card.
A more detailed answer would mostly consist of quoting the Comprehensive Rules Book verbatim, so I suggest if you want to dive in there, go straight to the source.
While Murgatroid and Alex P are right that a complete understanding of Layers would require a full quotation of the recommended references, there is a space here for a broad overview.
Magic has a lot of effects that modify permanents in play. Often times these effects can be confusing or mutually exclusive when stacked, so the rules for how to deal with modification effects are very detailed.
The basic concept is called the Layer System. At any point in the game when you have to understand what kind of object a permanent is you start with the base object and then apply all existing effects that are modifying (or could modify it) one at a time until they have all been applied.
The order in which these effects are applied is largely determined by the type of modification being done. For example, Type changing effects (like turning a land into a creature) are applied before rules changing effects (like giving a creature vigilance) which are applied before power/toughness adjusting effects (like giving a creature +3/+3). The categories of modification are referred to as "layers", and there are 7 layers with several subcategories.
Inside a layer or sublayer, order is determined first by dependencies (an effect that makes all lands creatures will be applied before an effect that makes all creatures goblins), and then finally by "timestamp", the time when the effect came into existence, with older effects being applied first. Newer effects can and will overwrite older effects if there is a conflict.
There are no distinctions between effects that are being granted temporarily ("until end of turn") by oneshot effects and effects that are being granted statically by a permanent on the battlefield. All that matters is the type of effect and the time the effect began applying.
The result of all this is a system that about 99% of the time works in the most intuitive fashion possible, and mostly only fails to be intuitive when there is no single intuitive answer (I'm looking at you, power/toughness swapping). That's honestly pretty impressive considering how many bizarre interactions it has to handle (Opalescencex2/Humility being the most famous).
