The Bologna Process is an attempt to standardize college education throughout Europe (The European Higher Education Area or EHEA). There are two ways this might impact US higher education. First, European schools have adopted some features of US colleges and universities- like degree names (BA, MA, PhD) as their standard. In other words as they restructure they have looked at what they think works as US institutions and have chosen to include those in the new structure. Second European schools will use this to market their higher education. The ease of transfer might make more students stay in Europe or go to Europe instead of going to US schools.
The actual process of making credits and degrees transferable has been developed over a decade and includes a lot of policy statements. I decided I did not need to learn the details during one of the busier times of my semester.