Final answer:
The statement that a package can be saved locally or shared using ArcGIS Online is true. Packages such as maps and geodatabases can be stored on a local machine or shared via the ArcGIS Online platform.
Step-by-step explanation:
A package can indeed be saved on your local machine or be shared using ArcGIS Online. The statement is true. In the context of ArcGIS, a package may refer to a collection of files related to geographic information systems such as maps, layers, geodatabases, and toolboxes. These packages can be saved locally for personal use or backups. Alternatively, they can be shared online through ArcGIS Online, which is a collaborative web platform designed by Esri where users can share and access geographic information and maps.