Plug-ins are basically software add-ons.
With an audio application such as an audio editor you might get a basic program that will cut, splice, crop, etc. but you want to add an effect to your project such as reverb, fade-in / out, reverse, etc. If these are not already an option within the software, some programmers will enable plug-in support. This allows you to "add" the required effect to the software at a later time.
The main types of supported plug-ins are DirectX and VST although product specific plug-ins are also available for programs like Winamp and Windows Media Player amongst others.