In the 1970s, NASA launched two spacecraft called Viking 1 and Viking 2 on missions to Mars. Both spacecraft photographed the surface of Mars and sent images back to NASA. In one photo, a hill on Mars' surface looked a little like a face. Author and conspiracy theorist Richard Hoagland went a step further and said that it didn't just look like a face, it was definitely a face. Hoagland theorized that an alien civilization colonized Mars and that the face was evidence of an alien city in the Cydonia region. When other satellites photographed the surface of Mars, the pictures of the Cydonia region revealed that the face was just an eroded mesa. Hoagland argued that the equipment NASA used to take the subsequent photos wasn't as accurate as the Viking equipment. He also claimed that NASA doctored the images, making them look less like a face [source: Hoagland].
We've since had a very good look at Mars's surface and the "face" turns out to be an illusion created by hills and shadows. Humans tend to recognize distinct shapes and patterns even from vague or indistinct shapes and objects. If you've ever seen a cloud that reminds you of a particular animal, that's an example. We call this tendency pareidolia, and there are several examples on Mars.