A world seed in Minecraft controls how world generation is conducted. The same seed generates the exact same world in compatible versions of the game.
Members of Minecraft@Home study in-game screenshots to detect unique structures that generate in specific ways in a world, and then search through millions of worlds to try and find that exact terrain.
Herobrine is a well-known hoax in the Minecraft community. The screenshot in question was posted alongside the original creepypasta story which gave birth to the Herobrine hoax.
The screenshot was taken in Alpha version 1.0.16_02 and features the player looking at a hill, with a chicken in the foreground and what looks like a player hiding in the fog in the background.
In their methodology document, the team describe terrain structures they used to find the correct seed.
Two large trees on the left side are described as
crucial to the seed cracking algorithm. This is because
compared to terrain, big tree seeds can be tested significantly faster than other structures.
Other helpful structures are the eight other trees in the image, which cannot be in the same area as a big tree, and the hill, which can only generate at certain coordinates.
In addition, the dirt texture tells you that our are facing south, and the emptiness of the inventory implies that the player is near the world spawn.
All of these elements combined help make the search not take years and years to complete. Even so, the search for this seed took four months, having started last September, with the seed being found on 16 January.
The seed in question is
478868574082066804, taken in Alpha 1.0.16_02, with the player at coordinates (5,71,-298). This version does not support entering custom seeds, so you will have to edit the world save data to set the seed. Minecraft@Home offers a pre-set world save file of this seed at the bottom of their project page.
The following video made by the team describes the search and results of this seed hunt: