An app server is a software framework. It is dedicated to do one task and includes programs, routines, scripts for the the construction of applications. An app server is used to manage business logic and works over http, https, gui, webserver and other protocols based clients. Examples of Java application servers - JBoss, Apache Geronimo, Weblogic. Zend offers an application server called Zend Serve for PHP applications. Zope is another app server written in Python. App servers are complex to design.
A web server only handles HTTP and HTTPS protocol and used to create html pages only. You can use PHP, Python, Perl cgi script for dynamic page generation. Web servers are easy to design. Examples of web servers - Apache, lighttpd, IIS, nginx.
See - App server, Web server: What's the difference? - JavaWorld