I have read the documentation and some other questions\' threads about this topic and I don\'t really feel convinced; I don\'t see clearly the limits of use of this tech
Its quite a general question and not directly related to a specific programming problem. But in my opinion good software is based on good design and therefore a good understanding and best practices. So your question is a good one for stackoverflow.
So, what about fragments. It took me a while to understand why you could or even should use them. As @pskink said, you can easily live without them. But if you are planning to rollout your software on different devices, you should definately think about fragments.
The screen resolution and density is not the only problem. Think about a smartphone. The screen is much smaller, so you can not present your app the same way as you can on a tablet. For instance a master detail flow. Left side, a list of elements and when you click one element, you will see details of that element on the right side. Easy to do on a tablet. But on a smartphone you would put the master-view into one fragment and the detail-view into another one.
You got two options to realize that scenario. Either programm different activities for smartphone and tablet but because they are actually doing the same logic, it's better practice to put the logic into fragments and reuse those fragments in two layouts (phone/tablet).