Badging is a game design element along with many others. The last couple of years badges have become popular. In fact, vendor often bundle them with the points, badges, and leaderboards approach (PBL). As everything in gamification, it can be useful or not so much.
A badge is nothing but a token of achievement. Think of it as a milestone: an observable, positive outcome of a work done well. Now, imagine if you got a badge every morning you show up for work. How much effort did you put into this achievement? If everyone gets this badge every morning they show up, how much is it worth? Nothing.
What if from now on, instead of promotions, you would get badges? Would you love to take them home and proudly share with your family? Sure…
The value of badges depends on how the society views the effort what they represent. If done well, and they deserve respect among peers, badges could be useful in motivation.
Real life application of badges? You may have heard of micro-credentials. The idea is taking on, mostly in the higher education and the tech world. The point of micro-credentials is that you take a course online on a specific skill, and receive a badge that you can display on your profile: http://www.centerdigitaled.com/higher-ed/Why-Micro-Credentials-Universities.html
Companies who want to provide digital credentials to their employees that can be transferred with them are using applications like Credly.