Probate is the legal process of validating a will and administering an estate under court supervision. In New York it begins by filing the will with Surrogate's Court in the county where the deceased lived, formally notifying beneficiaries and creditors, paying outstanding debts and taxes, and eventually distributing what remains to the people named in the will. The executor is the person responsible for shepherding the estate through each of these steps.
Not every asset has to go through probate. Anything held jointly with right of survivorship, accounts with named beneficiaries, and assets inside a living trust generally pass automatically without court involvement. Real estate that was held solely in the deceased's name almost always requires probate before it can be sold or transferred — which is why understanding what was owned and how it was titled is one of the first things to figure out.