JEF is meant to supply, on short notice, a small force (of a few hundred troops) that can be sent anywhere in the world to deal with a crisis situation that would benefit from immediate attention before it turns into something larger and more difficult to deal with. Closer to home, JEF could put a force of up to 10,000 troops (land, air and naval) into action quickly. This option appears aimed at Russian plans for surprise attacks like those used successfully against Ukraine in 2014 (successfully to seize Crimea) and less successfully in 2015 (to take the Donbas area of east Ukraine).
After the Cold War ended in 1991, NATO nations began planning rapid reaction forces based largely on using conventional forces for emergencies within or adjacent to NATO member nations. This concept was expanded with the formation of the EU (European Union) in 1993. That was because at the same time the EU was formed there was a major crisis next door in the former communist state of Yugoslavia, where a civil war had broken out. The EU was meant to be an economic/political union. The EU has purely European and had more European nations as members than NATO did. Despite the existence of NATO, plans were soon underway to establish some EU military cooperation as well.