Subordination refers to the order of priorities regarding claims to an asset should the borrower default on the debt secured by it.
When the term subordination is mentioned in mortgages, it almost always arise because the borrower has an interest on a second mortgage.
Either that, or an investor is exploring creative ways to strike a deal with another.
For example when a second lender might agree to offer the borrower a very attractive interest rate lower than the first lender on the condition that the first lender subordinates their claim.
This means that the first lender has to sign a subordination agreement to make themselves second-priority for claims. The second mortgage lender then get the first lien on the property.
A lender would seldom agree to it unless there is incentive to do so.
The debt with a higher priority is known as the senior debt. While the one with the lower priority is known as the junior claim.
In subordinate financing, a first mortgage is refinanced with a new loan while the second is left untouched.
This is illegal by default unless the second lender allows it with their subordination policy which would subordinate them below the new lender.
The reason being that by default, when a first mortgage is paid off (refinance), the second moves up to becomes the first. Making any new mortgage a second.