Off-balance-sheet (Wikipedia.org)

Some highlights:

Off-balance sheet (OBS), or Incognito Leverage, usually means an asset or debt or financing activity not on the company's balance sheet. Total return swaps are an example of an off-balance sheet item.
Differences between on- and off-balance sheets

Traditionally, banks lend to borrowers under tight lending standards, keep loans on their balance sheets and retain credit risk—the risk that borrowers will default (be unable to repay interest and principal as specified in the loan contract). In contrast, securitization enables banks to remove loans from balance sheets and transfer the credit risk associated with those loans. Therefore, two types of items are of interest: on-balance sheet and off-balance sheet. The former is represented by traditional loans, since banks indicate loans on the asset side of their balance sheets. However, securitized loans are represented off the balance sheet, because securitization involves selling the loans to a third party (the loan originator and the borrower being the first two parties). Banks disclose details of securitized assets only in notes to their financial statements.
The Banking Example

A bank may have substantial sums in off-balance sheet accounts, and the distinction between these accounts may not seem obvious. For example, when a bank has a customer who deposits $1 million in a regular bank deposit account, the bank has a $1 million liability. If the customer chooses to transfer the deposit to a money market mutual fund account sponsored by the same bank, the $1 million would not be a liability of the bank, but an amount held in trust for the client (formally as shares or units in a form of collective fund). If the funds are used to purchase stock, the stock is similarly not owned by the bank, and do not appear as an asset or liability of the bank. If the client subsequently sells the stock and deposits the proceeds in a regular bank account, these would now again appear as a liability of the bank.