The problem with our instinct is that it makes us believe that space is a sort of "stage" that events take place on. Our instincts mislead us.
There is true independence from both space and time with regard to the reference frame. In other words, if you're riding your bicycle down a path, then every stationary object you see (trees, river, etc) is actually independent from you on the most fundamental levels. That means that the trees and the river are aging slower than you are, and the airplane overhead is aging more quickly than you are.
How can this be? This sounds like nonsense, I know, but it's true. You age slower than the passengers in the aircraft above you, but the age differrence is so small that there's really no way you can measure this difference (read about the Lorentz Transformations for more info regarding this interesting fact)
Therefore, space is not a stage by which events take place on, but everything in space has it's own reference frame. The reference frame of the aircraft flying above is aging quicker than you, just as you--being a completely separate reference frame--are aging quicker than the bushes and river that lie along your bicycle path.
In closing I can sum it up like this: a reference frame is just that frame that has its own measurement of time and space. That's it.
Any reference frame that does not share your 'rate of time' (any reference frame that is aging slower or quicker than your frame) or 'measure of space' (any frame that has a 12" ruler that's either shorter or longer than your 12" ruler), is a separate and distinct reference frame from your own.