This means that , ex you rent with a contract for 5 years and after a few years you leave this appartement you can rent it to an other person for the rest of the contract .
here is a usefull link for all of you readers that have to hit the dictionary every so many words when reading spanish. http://dictionary.reference.com/
I have never heard this word in any other context but the one I'll explain below.
Traspaso means that the current owner has a mortage, what he is selling is his part of the property and leave you to deal with the bank on the other part. Which means that you have to either pay off the debt as part of the transaction or get approved for another mortgage.