Bootstrap is a front-end framework for building websites. It ships prebuilt CSS and JavaScript components that make building sites fast. It comes with all sorts of common components that every website needs such as a grid system, buttons, drop-down, responsive form elements, carousel (of course) and so much more. As a developer I don't want to spend time styling yet another button. I just want to know which CSS class to add to an "a" tag so it looks like a button and I'm good to go.
One complaint about Bootstrap is you can spot it a mile away because a lot of developers use the default look-and-feel. When you see the famous Jumbotron you know it's a Bootstrap site. But with a little bit of effort you can make your site look unique.