Because your layer package is now shared with everyone (public), anyone will be able to search for it and find it. They will be able to download the layer package and view it in ArcGIS Desktop clients, like ArcMap and Explorer Desktop. The layer package gets unpackaged automatically into its component parts. You can also send (email) someone a link to your layer package by copying the URL to the details page of the layer package (in My Content, click on the name of your layer package).
Presently, layer packages can only be uploaded and downloaded. There is no support for viewing the layer package in a web application. This is something we're working on. When we do release this feature it will likely be a premium feature (for a fee).
Thanks,
Mike