To start with, a framework is more like a tool box that has the tools to accomplish basic tasks e.g A carpenter's toolbox would contain hammer, nails, etc.
In my case, I use Laravel(just started learning Angular 2)
Laravel is a PHP framework that makes you app development simple and faster, it comes with the basic things you need to build your web app and more e.g:
more at laravel.com
UI frameworks like Angular, Vue, React etc
provide you with things like:
two-way data binding,
ajax integration (so you write less code to make an ajax call)
Easy way to manipulate the DOM(Document Object Module)
etc More at their various sites.
So it makes you write less code than you would writing your web app from the scratch, so you focus on your app logic plus they are fun to learn.
I hope this helps