To put it in a nutshell, GTUG stands for Google Technology User Group and it is a community where programmers meet to discuss and work with several Google developer resources and products. There will be regular events that are similar to events conducted at Google I/O each year to enable programmers to learn about various Google technologies without having to visit Google I/O each year. Visit http://code.google.com/ for full list of topics. In many events, you may even get the chance to interact with developers who have already programmed on any of these platforms in person.
A GTUG can take many forms — from just a few people getting together to large gatherings with demos and lectures, to events like code sprints and hackathons.