What exactly do I get when I purchase an older version of Mac OS X?

In the past you could buy USB physical media for Lion but the item you linked to is a redemption code delivered by email. You then have the ability to associate that purchase with one Apple ID of your choosing so you can download and install.

Apple offers pre-sales support if you need more questions about this (or any product) and the end user license allows you to run Lion redeemed from the store on all of the machines you own and control but likely no virtualization or time-sharing allowed. Full details are online if you want to read through things before ordering or calling pre-sales support.

• https://www.apple.com/legal/sla/

From the Apple Store page you linked for 10.7:

What you receive: An email with a content code for the Mac App Store.

You should be able to link the code to the Mac App Store, and, subsequently, your Apple ID.