A map package is both the data and cartography that make up an entire map compressed into a single file for easy sharing and movement.
Esri has a map package format (.mpk, .mpkx) that can be created in ArcMap and ArcGIS Pro. These packages can be used in ArcGIS for Desktop and ArcGIS for Runtime.
Other GIS software suites have various supports for the packaging of a map and data. The OGC standard has defined a GeoPackage which is starting to be supported by more and more software.