Instance
An instance on the Fediverse refers to a running copy of a version of a piece of software on some server.
The Fediverse is comprised of accounts, and software often must exist in order for these accounts to do anything at all, be it accept followers, accept content, push content upon request of the account holder, etc.
Anyone could write Fediverse software, but that is rather highly time consuming.
Instead, people opt to download existing software, and create a running instance of it on some server.
Examples of Fediverse software: