Probate is a legal process that takes place after someone dies. It includes administering a deceased person's Will, identifying proper beneficiaries for the deceased person's assets, having property appraised, and paying debts and taxes.
Only assets held individually, without a designated payable on death beneficiary, go through probate. For example — life insurance in your children's name would not go through probate at your death. Another example is a bank account with payable on death beneficiaries.
It is very important to note that probate cannot be avoided simply by having a Will. Probatable assets in a Will still go through Probate, however, they pass to the people whom you have designated as proper beneficiaries. If there is no Will, then the probatable assets will pass according state law.