One obvious advantage is that it's cheap enough to use as-is. One of the things that keeps me from caring much about Arduino is that it's too expensive to use for anything but experimentation: if I'm building more than a one-off, I'll always do a custom PCB.
For reasonable volumes that's still probably the best approach, but at $8 a pop this is perfect for throwing together some quick project.
By way of analogy: to me, an Arduino is a breadboard. If I use one at all, it's to play with a first concept, and certainly not for any kind of permanent use. If that's true, then this is kind of like solderable perfboard: not optimal, but good enough for many things.
It's a relatively huge amount of power in a tiny package, ready to roll. Many digital logic tasks that used to take a number of TTL/CMOS logic chips, or other devices can now be done in one inexpensive package.
A simple example: every week it seems, on the electronics forums, someone will ask how to do a simple, or a complex timing task and they will be pointed at various logic, or 555 timer chip designs.
Using something like this not only makes those projects simple, it provides a common frame of reference. If I can say to someone "go buy a Trinket from Adafruit and load this code into it and it will work cause I already tested it on my workbench" that provides a tremendous value because both I and the person I'm talking to online are working from a common platform.
For reasonable volumes that's still probably the best approach, but at $8 a pop this is perfect for throwing together some quick project.
By way of analogy: to me, an Arduino is a breadboard. If I use one at all, it's to play with a first concept, and certainly not for any kind of permanent use. If that's true, then this is kind of like solderable perfboard: not optimal, but good enough for many things.