To understand it you'll need to know roughly what an OS is. Very roughly speaking an OS provides a program with a way to access files, connect to the internet and launch other programs.
What docker does is make something a bit like a 'virtual' OS with its own filesystem, network and task manager, and then start running programs in it (which then may launch other programs).
Since you're not making a VM which must simulate all of the hardware, this is a lot cheaper. However since a docker container gets its own filesystem, network etc. it can do whatever it wants without any other programs getting in the way.
Among other things docker containers make installation a lot easier since a program will only ever see its own files (unless you explicitly add your own files to the docker container). To a large extent you also don't need to worry about installing any prerequisites, since those can just be put into the container.
Making a docker container is a bit (a lot) like installing a fresh OS, just putting the stuff you need in it and then copying the whole OS whenever you want to run the thing again. Except it's been optimized such that it takes about as much effort as launching a program, as opposed to a VM which needs dedicated resources and are generally slower than the machine that hosts them.