The Atlas Pass has been a much-discussed facet of No Man's Sky, and of all the information that's known about these mysterious objects, there is one specific rule echoing through the community. Do not sell you Atlas Stones. Do not sell them, do not dismantle them. Hold on to them. At the end of the game (which I won't spoil here), you will need 10 stones.
If you are following the Atlas Path, your first one will be found after a quest line that begins at a monolith. Search for monoliths on nearby planets and activate them. Eventually one will point you in the direction of a space anomaly. Warp to the system that holds the anomaly, and approach the ominous floating space prism, the atlas station. Go inside and walk to down the path to meet the Atlas, a data collective that gives you an atlas stone, as well as enough warp cells to reach the system you originally warped from.
Continue your journey through the stars, searching for space anomalies. Eventually, you will come across a spherical space anomaly with two friendly scientists inside, one of which will give you a blueprint for the Atlas Pass.
One prominent use for the Atlas Pass is that of unlocking the adjacent door to the main area of the Space Stations. In here, you'll find an upgrade station offering an inventory slot in exchange for compounding monetary compensation.