The SitePoint PHP blog has a recent post showing you how to get Xdebug installed and working with PHPStorm through a Vagrant installation. The Xdebug tool provides additional debug information on top of what PHP natively includes in its own error handling.
Xdebug is a PHP extension which allows you to debug and profile your code, view detailed and readable stack traces when errors happen, and much more. For a detailed walkthrough, see Shameer’s post. If you’re completely unfamiliar with it, you would do well to first install it following the procedures below, and then refer to the post linked above for a breakdown of everything Xdebug can do for you and your apps. In this tutorial, we’ll set up Xdebug with PHPStorm for Vagrant hosted PHP apps.
His guide doesn't actually include the installation of Xdebug via Vagrant as the VM he's chosen (Vagrant Homestead) already has it installed. If you need instructions on that, check out this other tutorial. He shows you how to enable it in Homestead and configure the extension to connect back out to your waiting PHPStorm client. He then moves on to the client side and shows how to connect it to the server through PHPStorm's own debugger configuration. He includes a bit of sample code to test the connection (a Laravel route) and checking that the breakpoint handling works as well.