Play 2.0 comes with Netty[1] built into it for making asynchronous requests, websockets and REST easier to handle. Netty is what replaces Tomcat unless you choose to use a third party plugin that builds your Play 2.0 website as a WAR file. Also, with Netty, it builds the entire site into a self contained module that you can run with one click anywhere you have the JVM installed (and the dependencies such as the DB if not using the built in H2). I found it useful for quick presentations or portability.
Play is a web development framework. It has the capability to run standalone using it's built in http server or it can output a .WAR file that can be run under containers like Tomcat.
and play 2.1+ can serve https as well http://www.playframework.com/documentation/2.2.x/Configuring.... In practice, play instances are behind a front end server such as nginx for load balancing, https, caching, and virtual hosting. Play's convention for stateless sessions makes it really attractive to scale by adding more instances to the node balancer.
No, it's mostly replacement for the spring-web/struts/jersey/etc. layer (though it also has its own templating layer to replace JSP or whaever). You can run it under tomcat if you want to.
[1] http://en.wikipedia.org/wiki/Netty_%28software%29