It's a story that typically involves a new start following an end. It could be about a character's journey of rebuilding or finding a new purpose after a major upheaval or the conclusion of one phase of their life.
The Beginning After the End manga has indeed finished. It provided a satisfying conclusion to the characters' arcs and the overall narrative. Maybe there'll be spin-offs or related projects in the future, but for now, the main story is complete.
In some 'beginning after the end stories', there could be a group of characters. For instance, a band of survivors after a disaster. Each of them has their own backstory related to the 'end' they've experienced, and together they are trying to figure out this new beginning. One might be a scientist who can contribute knowledge for rebuilding, another could be a strong fighter for protection, and so on.