In order to earn or unlock an Achievement, you need to claim your player slot at the beginning of a game. At the moment you claim, the game code or Scorbitron downloads all your previously earned Achievements to know where you are along the progress towards unlocking them. This information is saved in the Scorbit platform and travels with you no matter where you happen to be playing.
At the moment you unlock an Achievement, the Achievement is presented on the game's display. Modern machines like Jersey Jack Pinball will show an animated alert on the screen. A Scorbitron will roll an overlay of the Achievement on the DMD display. Games without displays can't show achievements, but they will still be visible on the app.
Example JJP Achievement
Example DMD Achievement
Also at the time the Achievement is unlocked, a notification is sent to the app as a push notification, and the Achievement appears in the Activity Feed. These Achievements are only sent to you, and will only be sent to your followers if they are very high level and difficult Achievements.
Achievement Push Notification and Activity Item