When a person establishes a Living Trust (also sometimes called a "Revocable Trust" or an "Inter Vivos Trust"), they have only taken the first step in implementing the Trust. The next step is to "fund" the Trust.
When a Trust is first set up, it generally has nothing in it. After setting up the Trust, the next step is to make sure that the Settlor's assets or property get into the Trust. Most estate lawyers call this "funding" the Trust. Funding the Trust can be done either by transferring ownership of assets into the name of the Trust or by designating the Trust as beneficiary or as what is sometimes called a POD ("pay on death") designation. Either way, the goal is to make sure the Settlor's assets and property get into the Trust without having to go through probate.
In order to understand this further, consider the following example. A person who establishes a Trust owns a home, a checking account, and a stock brokerage account. In order to fund the Trust with this person's assets, a deed should be executed and recorded transferring the home into the name of the Trust. The checking account should also be renamed in the name of the Trust. The brokerage account can either be renamed in the name of the Trust or alternatively, where available, the account can include a provision naming the Trust as the beneficiary or POD designee. If these steps are accomplished, when the person dies, all assets will either be in the Trust or will go into the Trust without probate.