JSON is just a way to represent a JavaScript object textually. If you've ever worked with object oriented programming, it can be compared to serializing an object. It is a good replacement for XML in certain applications, for example, a JavaScript client passing information to and from a server via AJAX. JSON is immediately usable by JavaScript as an object and so you skip having to parse XML when you're sending this information back and forth.
Most programming languages have support for decoding JSON either built in, or via a third party function. This makes it very simple to transfer objects between JavaScript and other languages with only one or two lines of code. I'm sure you see the power in that