A widget can be a software application, an element of interaction in a graphical user interface, or a web widget, which is in essence a software widget for the web.
As an element of interaction in a graphical user interface it is something like a button or a scroll ball. Each widget will facilitate a specific type of user-computer interaction.
A software widget is a something like a desk accessory or applet, this is basically a stand-alone user interface, in contrast with something like Microsoft Word, which is a much more complex application.