A blind trust is a trust that you can't control, and don't know how investments are being made. A blind trust is a trust that you can't see. You know you have it, you may get income from it, but you can't access it and you don't even know what is in it.
For example, if you have a situation where you have a fiduciary duty, or become a government official, then you might have a blind trust set up, like Ben Bernanke, the chairman of the Federal Reserve, who put all of his assets in a blind trust so that he can't see them. With a blind trust his decisions aren't affected by his personal wealth.
Another example of a blind trust is where parents give money to their children or grandchildren, but they don't want them to be able to see those trusts or know what is in them.
Sometimes, trusts are set up for buying assets and you don't want the seller to know who is buying. In this case, you might put money in a blind trust to make a deal, while hiding the purchaser's identity. This is a common business practice for real estate developers and movie stars, so the public doesn't know the details of their personal and private affairs. Blind trusts are often used by very wealthy people, so that their business dealings can't be overly scrutinized.