The US post office charges an extra fee, currently 22c, for items they consider to be non-machinable - square and other non-rectangular shaped envelopes, lumpy envelopes, etc. Additional ounces also cost 22c each for letters, up to 3.5 oz (yes, you pay 22c for that extra 0.5 oz after 3). If it is >3.5 oz it is not considered a letter, and you are charged package fees.
Where is this all going you ask? Well, the greeting card industry partnered with the USPS in 2010 to try and let people know when their cards are going to cost extra by placing a butterfly symbol in the stamp corner, and the post office has stylized butterfly stamps to cover that. These stamps are also square, to reinforce the non-machinable concept.
This is printed on many greeting card envelopes that are square, irregular, or will contain thicker cards requiring the extra postage. This symbol is printed slightly smaller than the stamp itself, making it easier to cover it up.
The USPS article about its introduction is here.
I've received the 2013 66c Spicebush butterfly (my favorite), and the 70c Great Spangled Fritillary. The new stamp which is non-denominated, and currently valued at 71c, features the Eastern Tiger Swallowtail. I haven't received that one yet, but I have a sheet of stamps waiting for the perfect envelopes.
I also spotted a Monarch butterfly on the Ohio stamp in the Flags of our Nation series.
The Monarch was also featured on the 64c butterfly stamp, the first in the series issued in 2010. Here's an image from USPS.
The 65c butterfly showcased the Baltimore Checkerspot.
VioletSky's post today reminded me of these stamps from the Insects and Spiders sheet - a Monarch caterpillar and butterfly. I showed this envelope in an earlier blogpost. If you'd like to see the rest of the insect envelopes and accompanying stamps (there are a few spiders thrown in as well), here's the link.