Relative paths store the location of the data source relative to the location of the map document. So instead of looking in the H:\GIS\myProject folder, the MXD file simply looks for data ‘within the same folder as the MXD file’, regardless of what the folder name might be. Files can also be stored in subfolders under the same project folder.
If you change your map to store the paths of the data sources to relative path names, the project no longer looks for the data using the entire path (starting the with drive letter). The user who is CREATING the file, not the user who has received the file, must make the change from full to relative paths. If the map also has data layers that do not meet the criteria (falling within the folders or subfolders of the MXD file location), those data layers continue to be stored with their full path names.