There are two basic kinds of softphone: a "fat" phone that's coded to run only on a full-fledged PC be that a Windows, Mac, or Linux machine. This software needs a real desktop or laptop CPU and all the other accouterments associated with a full-on PC in order to perform its functions. The other kind of softphone is one designed for a mobile device. Mobile VoIP clients are "slimmer" than a desktop softphone, which really just means they're designed to look a little different and probably have a few less features since mobile devices aren't as powerful as desktop machines. But if you're looking to run your home phone off your mobile phone wherever you are, then a mobile softphone is definitely the ticket; so be sure to investigate whether you residential VoIP provider offers a dedicated mobile client, whether that client will run on your mobile device, and how much it'll add to your monthly service charge.
From an end user point of view, the actual phone service works in the same way, you pick up the phone to answer a call or to dial a number just like with a landline service. Number porting means you can keep your existing phone number and simply switch it over to your new service provider. The residential VoIP providers take care of the call routing and you can call any destination and receive calls from anyone, just like with regular home phone service.