This week's book giveaway is in the OCAJP 8 forum. We're giving away four copies of OCA Java SE 8 Programmer I Study Guide and have Edward Finegan & Robert Liguori on-line! See this thread for details.
As Gregg says, Grails is primarily a server framework for web applications running on JEE servlet/app servers.
It is built on top of Java (Spring, Hibernate etc) and 100% interoperable, so you can do anything with Grails/Groovy that you can do with Java, because you can access all your Java libraries anyway. It also gives you easy access to more advanced JEE functionality, such as security, transaction services etc (e.g. via Spring).
But Groovy/Grails also make JEE serverside development much easier by providing masses of clever built-in functionality and "coding by convention not configuration" (no need for XML config files). The resulting web applications can be deployed as WAR files on any servlet engine or full JEE application server, from Jetty and Tomcat to Websphere.
And as well as the traditional benefits of Java as a robust and sophisticated application platform, you also get all the advantages of Groovy as a dynamic programming language.
Meanwhile, the view technology is GSP, which is basically JSP + extra tag libraries, and is also based on convention e.g. your view pages go in your "views" folder. But you can use other technology, such as Flex, AJAX etc if you want to.
The default URL mapping on the server is "/controller/action" (and your controller classes follow the same convention, with an "action" mapping to a method inside the controller), but you can extend/modify this however you like e.g. to create a REST-style interface (see chapter 11 of "Grails In Action" for examples of how to do this).
As for GIS, well, Grails allows you to do everything you could do with Java, but much more easily e.g. produce/consume XML (for interacting with W*S services perhaps), call 3rd party Java libraries for spatial data processing, talk to a spatially enabled database, talk to remote servers via REST/services/RSS/whatever, provide your own services via your own REST interface, etc etc.
You can use AJAX libraries for web-mapping, such as Google Maps or OpenLayers etc, as well as various plugins e.g. for Flex, so you can build a rich AJAX-enabled interface and support it via your Grails services in the same way as with any other web application.
I suggest you try some of the excellent online tutorials for Grails e.g. Scott Davis's "Mastering Grails" series on the IBM developerWorks website (including one on Google Maps with Grails). You'll be amazed how quickly you can get something running with Grails, compared to traditional Java tools.
So all you need to do now is figure out what you want to do, right?