Prestige Paths are a way to add another layer of flavor onto a character without using class levels. They are somewhere between a class and a background. Class levels are finite in 5e, so this allows for a light version of a class without breaking normal progression.
This is a primer containing some rule clarifications for using Prestige Paths. It also contains a sample Prestige Path, the Knight of the Chalice.
Feel free to leave any questions you have in the comments section.