Briefly, a trust arises when a property is held by a person 'upon trust' for another person. (It can be held by more than 1 person, and can be held for more than 1 person). E.g. A may hold property on trust for B. A will be the 'trustee', and B the 'beneficiary'. The beneficiary is the person who is entitled to the benefits of the trust, so e.g. if it is a house, B may eventually use the house, or sell the house, whereas A will be considered a bare owner and must not use the estate for his/her own benefit.
Under trusts, there are essentially two owners because of this. Historically, trusts were not recognised by common law, and if the trustee did use the property/estate for his/her own benefit, there would not be much you could do about it. Equity eventually protected the beneficiary, who has a right enforceable only in equity (not at law).
I suppose looking at it from a normal persons perspective, it lives up to its name in that if somebody uses a belonging of yours when they've been expressly told not to, or you have not permitted it, they've breached your trust, and vice versa.
(This is trusts VERY briefly, and I tried to make it more understandable to people who don't study law. I've literally taken all of this out of my law book, with the exception of the last paragraph above this one, and I've changed the examples demonstrating it ever so slightly, so here's the reference: Judith-Anne MacKenzie and Mary Phillips, Textbook on Land Law, 13th edition, 2010, Oxford University Press.)