On Sol 32 (Sept. 7, 2012) the Curiosity rover used a camera located on its arm to obtain this self portrait. The image of the top of Curiosity's Remote Sensing Mast, showing the Mastcam and Chemcam cameras, was acquired by the Mars Hand Lens Imager (MAHLI). The angle of the frame reflects the position of the MAHLI camera on the arm when the image was taken. The image was acquired while MAHLI's clear dust cover was closed.
That's from NASA's description of this great Curiosity self-portrait.
What really stuck out to me, though, was the use of "Sol 32". Sol is what you call a "day" on Mars. We use a different word because the length of time is also a bit different. One Martian Sol is equal to 24 hours, 39 minutes, and 35.244 seconds. Sol 32 isn't, itself, a date, but simply a record tracking the number of sols that Curiosity has been on Mars—starting with Sol 0, which was August 6th. Every mission to Mars since Viking has kept its own sol count, so you can't really use these sol dates to keep track of history except as it relates to a specific mission.
There have, however, been proposals for a standardized Martian calendar system with a starting point that all dates progress from. NASA includes a Mars Sol Date on its Mars24 Martian clock app. In this case, the count begins on Earth date December 29, 1873 at noon Greenwich Mean Time and MSD represents the number of sols that have happened since then.
Why December 29, 1873? The Mars24 explainer just says that this date was chosen because it precedes all the really good, detailed observations of how time worked on Mars—how fast the planet was spinning, how often it went around the Sun, what the orbits of its moons were like ... that kind of thing. In 1877, the orbit of Mars took it particularly close to Earth, allowing humans—and their increasingly good quality telescopes—to get a really nice view of the planet.
That still doesn't exactly explain the 1873 date, though. But, according to Wikipedia, it's also the birthday of Carl Lampland, an American astronomer. Among other achievements, Lampland would calculate temperatures on the Martian surface, finding a large difference between soltime temperatures, and those at night. That data gave scientists their first clue that Mars had a particularly thin atmosphere, compared to our own.