Honestly can't explain how it works because I hate them, but just scroll through the last 3 pages of threads and you'll find at least 4-5 threads in detail with a little bit of confusing math.
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First, players have a common egg. Some players get more pink eggs than blue, others get blue over pink. This only affects what color box the 300 golden eggs are located. The 300 golden eggs will be in your uncommon egg box color. So with this, you will be opening more common egg colored boxes, if you wish to get eggs to open uncommon egg colored boxes, you will have to trade your common egg colored eggs. You do this by placing your eggs in neighbor's baskets. You put in 100 eggs, you get 50 back. If your common color is pink, and want blue eggs, you will need to place your eggs in a pink basket.
You get baskets by buying them for 10 donuts, OR if you are lucky, you will get some by tapping bunnies (I've gotten 5 by tapping bunnies, 2 pink, 3 blue). Once you get a basket, place it in your Springfield and your neighbors can now trade in their eggs in your town. You can't collect until your basket is full (4 eggs fill up the basket, those 4 eggs = 400 eggs)
The part i'm still confused about is that it said the trades are 100 to 50 (100 eggs from your neighbor, in exchange for 50 of yours) The times i've traded eggs, I immediately lose the 100 eggs in exchange for the 50, but my neighbor's egg count remained the same after the trade. So I don't know if they have to give 200 eggs when they collect the basket.
It's... let me think... it's as though they all come with 200 eggs that can only be used for these "trades" with neighbors. So, if I find a pink basket, it has 200 invisible blue eggs in it that can only be accessed by my neighbors who put pink eggs in it. I never see the blue eggs, and don't have to give up any of my own, I just get to collect pink eggs once they're all traded away.