ArcIMS (standing for Arc Internet Map Server) is a Web Map Server produced by Esri accessible through a web browser.
Sometimes these maps are just static images allowing simple panning and zooming, while others are more complex pages.
The core of ArcIMS consists of a spatial server which processes most of the map-related services.
ArcIMS uses Esri's ArcXML to receive and respond to requests from the client.
The data behind ArcIMS is usually stored in Shapefile format (an open specification) or in an ArcSDE RDBMS database.