What is the use of map package ?

It is easy way to share your map with others. map package in ArcGIS is a ZIP file contain the follows:

1- Map document

2- Layers in the Map Document

3- The Symbology used for these layers

4- The Data Source for these layer

Therefore, when the user double click the map package it extract locally on the user PC and open map document exactly like your export

So, don't worry about your data source or if this data absolute or relative path. Map Package do that for you