A widget is simply a small set of computer code that does a specific thing on a webpage or computer. For instance, the clock (assuming you use it) on your computer is a widget. On a website, the code that keeps the advertisements running is a widget.
These little bits of code are called various things; widgets is just one of their names. Essentially, they are non-primary code that adds utility to a desktop or webpage.
An iPOD is a music, and video player. Some iPODs only do audio, some do both. Some have internet connectivity, and some can use various widgets which in this case, are called "apps." iPOD is specifically an Apple product. Other companies produce what are generically called MP3 players (MP3 being the music format used by most players, but not iPODs). Microsoft's version is called the Zune.