A plugin is a portion of software code [basically an add-on or extension] which enables certain elements of a webpage to load. Plugins are available for all different applications on a website, and can also be added to a new or existing one.
Plugins allow more complex site content to be displayed and function properly [e.g. animations and games] which may not have been possible otherwise.
Plugins are generally free downloads provided by certain software providers [they might prompt a download their plugin upon landing on their site]. Some can be malware however if it is from a trusted provider and a program which you will use it is worthwhile downloading the plugin. A quick online search will reveal the reputation and/or quality of the plugin.
Examples of popular plugins include: Adobe Flash Player, Macromedia Flash Player, Quicktime Player and Acrobat Reader [for PDFs].