| The woo is out there|
|Aliens did it...|
|... and ran away|
The "Arecibo answer" is a crop circle (well, crop rectangle, to be accurate) that is purported to be a response to the "Arecibo message", a piece of coded information about Earth and humanity which was first beamed into space in 1974. It appeared in 2001 near the Chilbolton radio telescope in Hampshire, UK. Despite the fact crop circles are known to be hoaxes, people still believe that this is key evidence of extraterrestrial presence on Earth.
The crop circle is a near replica of the Arecibo message, which contained various pieces of information such as the numbers of chemical elements, the composition of DNA, the position of Earth in the Solar System, and a depiction of a human being. The "answer" itself doesn't expand much upon this and still forms the same 23 x 73 grid (because these numbers are primes) and most of the chemical data remains the same. The changes to the message to create the response are straight from existing alien folklore and science fiction. In the section detailing important chemical elements, the main focus is altered from carbon to silicon, and the diagram of DNA is re-scribbled slightly. At the bottom, the pictogram of a human is replaced with a shorter figure with a large, bulbous head. This is a clear reference to the "grey" type of alien, and as a depiction could only be something that a human came up with.
The likelihood of the Arecibo message ever being picked up is very, very low. It was aimed at globular star cluster M13, which is 25,000 light years away. In fact, it's so far away that in 25,000 years when it finally reaches its destination, its destination will have, in fact, moved! The message was only intended as a demonstration of the transmission technology, not as a serious attempt to make contact.
The message does also pass close enough to a few nearby stars to have been potentially "received" in their vicinity. But why wouldn't the recipients simply send back a message via radio, instead of coming here and messing up some poor farmer's crops at night and then sneaking away?
So why wouldn't the recipients simply send back a message via radio? If they are aware of the general situation on Earth, they would know that an answer sent back via radio might be hidden from the public as many other encounters before, which have been well-documented and, meanwhile, disclosed. Crop formation is the simplest way to answer for everyone to see and hard to hide.