I have come across the terms on several occasions however am unsure what they mean exactly.
They refer to DNS GLUE records. Generally, they're used by the TLD domain name servers to respond to a query with both the name and IP address of the name server for the domain you ask for.
For example, if you ask the .com name server for "example.com", it will respond with a glue record along the line of "ns1.example.com 10.20.30.41"
It will actually come back as a set of separate records, so a query to the .com. name servers for the name server of example.com will look like this:
@Hyppy's answer covers what glue records are.
The other bit of your question is mismatched glue. This is what you get when the glue records held by the parent zone don't match the
[technically those records in your own zone aren't glue - that term only refers to the non-authoritative data held by the parent zone].