Windows Update Delivery Optimization was introduced with Windows 10 to make it quicker for end users to receive patches and other updates through Windows Update.
The concept behind Delivery optimization is a peer to peer network, either locally on your own network or across the Internet between other Windows 10 users and their devices, that speeds up the delivery of these updates by retrieving them from these other machines to shorten the distance between source and destination machines. Shorter distances means quicker downloads of the updates and patches.
By default on a new installation of Windows 10 Home or Professional Delivery Optimization is turned on however, you have control over keeping the option turned on or choosing to get updates just from machines on your local network or from other Windows 10 PCs on the Internet.
When many users hear about Delivery Optimization in Windows 10 their first concern is security, privacy and then followed by concerns about using up limited bandwidth to serve updates out to other Windows 10 devices across the Internet.
Microsoft addresses the first two concerns, security and privacy, in their Windows Update Delivery Optimization FAQ...