According to Wikipedia:
In computer programming, a widget (or control) is an element of a graphical user interface (GUI) that displays an information arrangement changeable by the user, such as a window or a text box. The defining characteristic of a widget is to provide a single interaction point for the direct manipulation of a given kind of data. In other words, widgets are basic visual building blocks which, combined in an application, hold all the data processed by the application and the available interactions on this data.
In WordPress, widgets are commonly referred as to elements in either the sidebar or the footer (but they can occur anywhere on your page) that contain small blocks of additional data like your latest tweets, a video, a collection of Social Media icons, etc.