It's popular because it's free and it's open source. The hardware is open so you can build an Arduino compatible board yourself (with compatible I mean that it fits with all the shields available) or you can just use the appropriate ATMEL microcontroller on a design of your own. The bootloader that sits in the microcontroller is free and the IDE and compiler are free.
Contrary to what some believe there is nothing special or propriatary with the "Arduino chip". It's just an ATMEL microcontroller with a bootloader flashed to it. There's no interpreter (like on the BasicStamp) on the chip.
The "Arduino language" is more or less C which, weather we like or not, is the "industry standard" programming language. I've never played with the Arduino (because I use PBP and I don't know C) but I'm pretty sure there are orders of magnitudes MORE info and examples available for the Arduino than there is for PBP. "Everyone" is using it.
Not saying anything is "better" than anything else but these are some of the reasons for its popularity. Personlly I prefer PBP because I have it and I know how to use it (most of the time) - but it ain't free.
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