An "open source web application" indicates a couple of things. One, that the code is freely available to use and or modify under some sort of open license (GPL license or its variants, BSD-style license, MIT License, Mozilla License, Apache License, etc). Secondly, that the application is web-based, but that doesn't seem quite right. Are you sure it didn't say "open source web development application"? Or maybe it includes a server that runs locally, so technically it IS a web application.
A component library is a set of classes/methods/functions that serve a general-use purpose. For example, I've used eZ Components in some in-house work to draw data graphs. So this statement would seem to indicate that Zend Studio has some built in "modules", or similar components that you can use to do certain things.
HTH,
