"ITF" in banking stands for "in trust for." It means that the owner of the account is acting as the trustee of the funds, which transfer to the beneficiary of the account when the owner dies.
"In Trust For" accounts are a method for someone to ensure that the funds in his bank account transfer to someone else with little difficulty if he passes away. The owner of the account retains control of the funds as long as he lives and is permitted to make changes at any point. Banks in some states prefer to use the "payable on death" designation, which also pays the balance of the account to one or more beneficiaries when the account owner passes away.