Probate is the process of "proving" a Will.  Your Executor (the person responsible for administering your estate) takes your Will to the Courthouse and "proves" it genuine by registering it, filing affidavits and notifying the known heirs.  Then the Executor posts a bond and reports to the court with an inventory of all your assets.  Finally, after about a year, the Executor distributes your assets and reports back to the Court accounting for every receipt, every cancelled check and every invoice.  It is an accounting nightmare.  All this is on the public record making it easy for predators to identify rich and vulnerable prey. 

Probate can be costly and time consuming.  Court fees, professional fees and commissioners fees can be expensive.  The estate is open for one year, so some assets (like real estate) get tied up and might not be distributed.  If you own property in another state, you must also go through the probate process there.

There are ways to avoid probate.  Usually this means establishing a Living Trust.  You put all your assets in the Trust and you are the trustee controlling them.  When you die, the Trust assets don't go through probate but continue to be administered in the Trust by the person you have named as the successor trustee.  This saves your heirs from the expense and delay in settling the estate through probate.  Trust assets can be distributed in a few weeks not years, and at very little expense.  As an extra bonus, a Trust keeps your affairs private where the probate process makes them part of the public record for everyone to see. 

Conservatorship is administering the assets of a person under a disability.    First, you are declared incompetent and a conservator is appointed by the court.  The conservator must file an inventory, post a bond and report income and expenses periodically.  This is another expensive accounting nightmare and you don't get to pick your conservator.  A Living Trust allows you to name a conservator and removes the administration from court control.