What is meant by "nonclustered legacy instance of SQL Server"? When I research nonclustered legacy instance in SQL Server, all I get is some results about indexes. This is obviously not related to or affiliated with indexes, so what is meant by "clustered instance of SQL Server" and nonclustered ones?

Context: SQL Server 2014 Upgrade Technical Guide (pdf download)

Example extract:
non-clustered just means it's not part of a Failover Cluster Instance ("FCI" -- which is fundamentally different from a Windows Server Failover Cluster ("WSFC")). An FCI requires a WSFC, but the opposite is not true. A non-FCI instance of SQL Server is typically called a standalone instance. A standalone instance can be installed on a WSFC (and take part, or not, in Availability Groups). You can see how they work together here. 

legacy is not a special word here, it is just an adjective that means older. There is no more meaning to "legacy instance" than there is to "ancient instance" or "deprecated instance" or "no longer supported instance." In this context 2005, 2008, and 2008 R2 are mentioned explicitly, but 2012 would be in that bucket as well.

The doc portion you reference just means you can't convert a standalone instance of SQL Server to a clustered instance as a part of an upgrade.