A trust, like a corporation, is an entity that exists only on paper but is legally capable of owning property. A flesh-and-blood person, however, must actually be in charge of the property; that person is called the trustee. You can be the trustee of your own living trust, keeping full control over all property legally owned by the trust.
There are many kinds of trusts. A "living trust" (also called an "inter vivo" trust by lawyers who can't give up Latin) is simply a trust you create while you're alive, rather than one that is created at your death under the terms of your will.
All living trusts are designed to avoid probate. Some also help you save on death taxes, and others let you set up long-term property management.