Probate is a legal process that takes place after someone dies. It includes: proving in court that a deceased person's Will is valid or distribution of assets when a person dies without leaving a Will.
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 if one exists 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.
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.