A trust is a legal entity set up to hold assets - cash, investments, real estate, etc.
There are three essential parties to a trust: the grantor (trustor) who sets up the trust, the trustee who manages the trust, and the beneficiary - the party for whose benefit the trust exists. Often, the trustor and trustee are the same party. Trusts can be revocable or irrevocable. They are very flexible and the conditions/restrictions can be set up as the trustor desires. So your question about "how exactly they work" depends on the specific trust.
It's money that's been set aside in your name, usually as part of an inheritance. If properly managed, it should grow with time until it's released to you, in which case you're responsible for it.
How exactly do they work? Is there a set amount of money in it or does the money continue to grow for the rest of that person's life?