Probate is a legal process that takes place after someone dies. It includes:
proving in court that a deceased person's will is valid (usually a routine matter)
identifying and inventorying the deceased person's property
having the property appraised
paying debts and taxes, and
distributing the remaining property as the will (or state law, if there's no will) directs.
Typically, probate involves paperwork and court appearances by lawyers. The lawyers and court fees are paid from estate property, which would otherwise go to the people who inherit the deceased person's property.