A map element that defines display properties for one or more layers in ArcMap.
A "data frame" in ArcMap is a map element that defines a geographic extent, a page extent, a coordinate system, and other display properties for one or more layers.
The properties of a data frame define the context for any spatial data in ArcMap. These include the coordinate system, geographic extent, measurement units, scale, the drawing order of layers, and more. Many of those can be set in the Data Frame Properties dialog box. Whenever data are added to a map, they must be added into a specific data frame.
Many cartography texts use the term "map body" to refer to what ESRI calls a data frame. The term is also used with completely meaning in different contexts (e.g. in R).