Dempster-Shafer theory is a way of talking about stuff we don't know for sure, even when we think we do. Basically, it's like having a buddy help you make decisions when you don't know what to do; like when you're stuck between two different options and you can't decide which one is better.
Dempster-Shafer theory takes all the information we have about a situation and puts it into 4 pieces. The first piece is called belief. Belief is what we think is most likely to happen. The second piece is called plausibility, which is when something might happen, but it's not very likely. The third piece is called uncertainty, which is when we don't know what's going to happen. The last piece is called ignorance, which is when there's no information at all.
Then, Dempster-Shafer theory helps us figure out which piece is the most important based on how sure we are about each one. So if we're really sure about something (belief) and not so sure about something else (plausibility or uncertainty), Dempster-Shafer theory can help us make the best decision.