What do I need to know to allow players to edit assets from within a game in the unreal engine?

There is a whole lot you would need to learn for a feature like that.

1. How to use the Unreal Engine in general, because that's a foundation for each of the following steps.
2. How to build UIs, because you are probably going to need some tool palette.
3. How to create and change a procedural mesh.
4. How to detect mouse interactions in the game's viewport and associate them with a specific vertex, edge or surface of the procedural mesh the player is pointing at.
5. How to create a shader that highlights individual vertices, edges or surfaces of a 3d mesh, because you probably need some way to visualize what the player has selected.
6. How to change textures at runtime, because you are probably going to need a way to paint textures.
7. How to save mesh data and textures to a file. Either by implementing a standardized 3d model format of your choice or by inventing one of your own.
8. How to load mesh data and textures from those files.

This is really just scratching the surface, though. The tools you want to "replace the combined forces of" are sophisticated pieces of software that had probably a whole lot of professionals working on them for years. Replicating their whole feature-sets is probably not something you can do on your own over the course of a couple weekends.

What do I need to know to allow players to edit assets from within a game in the unreal engine?

There is a whole lot you would need to learn for a feature like that.

1. How to use the Unreal Engine in general, because that's a foundation for each of the following steps.
2. How to build UIs, because you are probably going to need some tool palette.
3. How to create and change a procedural mesh at runtime.
4. How to detect mouse interactions in the game's viewport and associate them with a specific vertex, edge or surface of the procedural mesh the player is pointing at.
5. How to create a shader that highlights individual vertices, edges or surfaces of a 3d mesh, because you probably need some way to visualize what the player has selected.
6. How to change textures at runtime, because you are probably going to need a way to paint textures.
7. How to save mesh data and textures to a file. Either by implementing a standardized 3d model format of your choice or by inventing one of your own.
8. How to load mesh data and textures from those files.

This is really just scratching the surface, though. The tools you want to "replace the combined forces of" are sophisticated pieces of software that had probably a whole lot of professionals working on them for years. Replicating their whole feature-sets is probably not something you can do on your own over the course of a couple weekends.