Mars 3 was part of the Soviet Mars program.
That whole program consisted of 2 mission: the Mars 2 and Mars 3. Both had identical rockets, orbiters, landers and rovers. Only difference is the launched at, which was 9 days apart.
The goal of the program was to reach Mars, start orbiting the ref planet, image the surface and put a rover on Mars.
The US had beaten them to the first goal. The Mariner 9 had gotten first into Mars' orbit.
But there was still the possibility of that other, bigger goal: getting to the surface of Mars.
Mars 2 failure
A couple of days earlier, the Mars 2 had failed it's descent towards. The lander was destroyed on impact.
The theory was that the entry had been at too steep of angle, causing the parachute deployment to malfunction.
So all hope were on the Mars 3 to achieve the goal for the Motherland.
Mars 3 Descent
On 2 December 1971, the Mars 3 lander started making it's way down through the thick dust storm that was going on at the time.
The lander entered Mars atmosphere at about 5.7 km/s. With the help of retrorockets, parachutes and aerodynamic braking it landed safely on the surface!
If you're curious what that would have looked like, check the video below to see the descent of the Mars Curiosity rover in 2012:
Mars 3 Operations
90 seconds after landing, the landing started sending information the the Mars 3 orbiter, which acted as a relay to send communications back to Earth.
But after 20 seconds, the transmission stopped.
There are a couple of theories why this happened. It could be a technical fault with the lander or orbiter.
Or the dust storm that was raging on the martian surface could have damaged the equipement or hampered it's ability to send back data.
The First Look At Mars' Surface
As part of that 20 seconds, a partial image was transmitted:
The first image of Mars' surface
The photograph was taken with a cycloramic camera, so the get the positioning right, you would have to rotate the picture 90 degrees clockwise.
Then it appears to show a horizon and dark sky, but according to the Soviet Academy of Sciences there is nothing, horizon or otherwise, identifiable in this photograph
For the first clear picture, the world would have to wait 5 more years when the Viking 1 lander arrived:
Exact location of the Mars 3 Lander on Mars
On 11 April 2013, NASA announced that their Mars Reconnaissance Orbiter (MRO) could have imaged the Mars 3 lander hardware.
The images were further picked apart by space enthusiasts and they identified all of the hubris: the parachute, a retrorocket, and heat shield.
In the years following, many scientist have speculated what exactly the Mars 3 image was showing.