User blog comment:BonesMcGee/Brainstorm: Potential savings in using the hurry hatch trick/@comment-173.216.161.166-20120905021903/@comment-5355974-20120905042859

"Peeking" is performed after you have obtained an egg with an 8, 10, or 13 hurry hatch.

Basically, depending on what type of device you use, you put your phone into airplane mode (aka a no-data/no-wifi state) while Tiny Village is running. Once you have done so, you will receive an error message that says something to the effect of "you have lost connection to the server." At that point, you go to your dino den and spend crystals to hurry hatch the dino. Once you see what your dino is, you 1) exit the game, then 2) force stop or force close Tiny Village, and then 3) turn off airplane mode so your data/wifi is back on. The order of these steps is essential. Do no flip-flop steps 2 and 3. Finally, you re-launch Tiny Village and you should notice that your dino egg is still hatching and your crystals remain unspent.

So now you know what dino egg you have without really having spent the time and crystals to find out. That's peeking.