Just as a layer package bundles the data for a layer together with its property settings, a map package bundles all the data associated with the layers contained in a map plus the property settings for those layers. So, a map package bundles everything that you see in a map together into a single file with a .mapx extension.
Map packages provide an easy way to share an entire map with others who may not be able to connect to your data sources. One thing to consider though is size. Because a map package will contain all the layers and their referenced data within a single file, it is possible for them to get very large.
I have personally created one for a client that was over 20 GB in size. The reason for it being so large was that the client had pictures stored in the database of the features. In addition, the map included local aerial photography. So when the map package was created it included the layers, the layer properties, the attached...