A subordinate mortgage is a mortgage that is of a lesser priority, or one that is held subordinate to, a primary mortgage. A good example of this would be a second mortgage, or even a third one. The second mortgage is subordinate to the primary, and the third mortgage is subordinate to both of those, etc. etc.
What this means that if the home goes into foreclosure, the primary mortgage will be paid off first. Then, if there is any money left over, it will pay off the second mortgage. If there is any left after that, it will go to the third mortgage (if there is one)… and so on.
It is much tougher to get a second mortgage than it is to get your first mortgage, but it is even harder than that to get a third. Also, the more mortgages you have on a home, the higher the interest payments will be. This is partly due to the risk involved. Since in the event of a foreclosure it is highly unlikely that a second or third mortgage will be paid off, the risk is countered with higher fees and more excessive interest rates.
So, if you had a property which you still owed $100,000 on from the first mortgage, but you also had a subordinate second mortgage on it, and it went into foreclosure, this is what would happen. If the home sold for $90,000 at auction, then all of it would go to pay your primary mortgage… leaving no funds to pay off the secondary mortgage.