You will find plenty of articles about Docker on internet.
That is why I won't explain you what IS Docker, but more why you could, and maybe should, use is as a web developer.
Let say you are working on a MEAN stack.
So you have Node, Express, Mongo and Angular in the project.
It is a lot of dependencies.
Some of these dependencies are in the package.json file, and some in bower.json file
The thing is, if you use a CI (Continuous Integration) like system, you will prevent possible human issues.
During a project development cycle, sometime, you have to change things in the project's settings.
If you run your application only on your computer with the normal way, you could install dependencies, forget to add them to the package.json and push you code on the repository.
The result will be that on your CI (Jenkins or another), the project build will break.
The real interest of using Docker is mainly to prevent this kind of issues.
It will simulate a CI system and will warn you about them.