Using WordPress to wrap a php application

I have a wordpress website up and running with my custom theme. I know enough PHP/MySql to build an application. What I would like to do is create/place the php code in(?) a page(?). Is that possible or is it gonna just be easier to code everything manually -as in the look and feel. I mean – if page links change how does that work? Or is there any way to place the app folder(php/html/etc) in the wordpress directory/theme directory and use the wordpress tags?

I hope I’m explaining this properly…