Lets see if this analogy helps, Jenny. Think of Invariant Representations (IRs for short) as puzzles. Each IR is made up of many puzzle pieces, all tied together with pieces of string going from piece to piece, and together they depict something we've encountered, either through our senses or our thoughts. When you think of something, you trace along those pieces of string until the entire puzzle is put together. If it's the very first time you're encountering this thing, the puzzle pieces and threads will be new (but inevitably linked to something).
If it's not the first time, you're just tracing the existing strings and putting the puzzle together. Those pieces of string get thickened each time you recall the puzzle they're part of, forming a a more easily recognised, and therefore clearer picture.
Tracing those threads to either form, or recall a puzzle set, is what goes on in the mind. The puzzle pieces and threads themselves are the brain.
The puzzle is never complete; one set of pieces may connect to another set, or form part of a bigger set, each depicting things which are related in some way. It could just be a very weak relation, like a connection of only a few small, thin threads.
Those "a-ha" moments that Steve mentioned are like establishing a strong connection between two (or more) previously unrelated puzzle sets. This creates a picture which, while you can see it includes the previous two, now looks completely different. Physically there are still distinct puzzles, (the original IRs haven't changed) but they now *also* combine to form a new one.
Kinda like doing a real puzzle. You have one section which looks vaguely foresty, and another section which could be clouds, or ocean, and another bit which looks like white cloth. At some point you see the separate sections a little differently and suddenly realise that there's a cabin in the forest, and the white cloth is the top of a mountain, and that's not ocean but a lake, and the left over grey/brown/green pieces are the base of the mountain, and it all comes together to form the scene of a beautiful lake/forest/mountainside retreat.
(and even better, you beat your Grandma's old record of 44 minutes!)