A bank, management firm, or other third party is given complete discretion to make investments on behalf of trust beneficiaries. The beneficiary is not informed about the holdings of the trust, and is therefore "blind" as to what the trust is invested in.
Blind trusts are used to avoid conflicts of interest between the beneficiary and the investments. Politicians and others in sensitive positions often place their personal assets into blind trusts to avoid public scrutiny and accusations of conflicts of interest when they direct government funds to the private sector.