A fragment is way more than just a view. In fact it can even be totally without a view. It can have all sorts of stuff in it including AsyncTasks, various Listeners, file and database access and so on and so on.
Think of it as a small activity, but you can have multiple of them on the screen and work with them all including communicating with each other while they are visible.
E.g. you could have a list of shopping cart displayed in one fragment and the currently selected cart in detail in another fragment. You then e.g. change the quantity of an item in the detail view and the list view could be notified about it and update the total price in the list view. You can totally orchestrate interactions like that nicely while e.g. still having only one of them visible on a smaller screen device.
I have refactored a large business app (>15 activities) from activities to fragments to get good tablet support and I would never start a new app without fragments.
Update Feb 2016: While the above still holds true, there are complexities with fragments that caused many people to entirely avoid using them. Newer patterns such as usage of MVC approaches and more powerful views provide alternatives. As they say .. YMMV.
