Probate usually works like this: After your death, the person you named in your will as executor -- or, if you die without a will, the person appointed by a judge -- files papers in the local probate court. The executor proves the validity of your will and presents the court with lists of your property, your debts, and who is to inherit what you've left. Then, relatives and creditors are officially notified of your death.
Your executor must find, secure, and manage your assets during the probate process, which commonly takes a few months to a year. Depending on the contents of your will, and on the amount of your debts, the executor may have to decide whether or not to sell your real estate, securities, or other property. For example, if your will makes a number of cash bequests but your estate consists mostly of valuable artwork, your collection might have to be appraised and sold to produce cash. Or, if you have many outstanding debts, your executor might have to sell some of your property to pay them.
In most states, immediate family members may ask the court to release short-term support funds while the probate proceedings lumber on. Then, eventually, the court will grant your executor permission to pay your debts and taxes and divide the rest among the people or organizations named in your will. Finally, your property will be transferred to its new owners.
To learn more about the probate process--and reasons for avoiding it--see Nolo's article Why Avoid Probate?