An estate is a legal person (like a corporation, as opposed to a natural person) which owns all the property and obligations of the natural person. Being a legal fiction rather than a human mind, it can't make decisions on its own. So estates have executors, a natural person who is authorized to sign on the estate's behalf. Sort of like the officers of a corporation. But this person does not have free reign - she is legally required to obey the will (if a legally valid will can be found), otherwise she is bound by certain assumptions codified in law (the default settings of a will, so to speak). A will can appoint an executor, or one (who may be a state agent, or a family member) can be appointed by a judge in the absence of a will.

Sort of like how a CEO has a fiduciary duty to shareholders and cannot just transfer the company's assets to himself (even though he technically has access to them), the executor has a fiduciary duty to the fictional legal person of the estate. Generally the will is binding, unless it is otherwise illegal. However, creditors must be paid first before the will is honored. Tangibly, that means the bank will give the executor the ability to write checks against the dead person's bank accounts. The executor has to provide death certificates to i.e. Comcast and Verizon to cancel accounts, pay the last bills, pay parking tickets and fines, and if there is anything left execute the will. This is not really the executor paying the bills though, it is the executor causing the estate to pay the bills.

If you're rich you have your law firm do it, otherwise a family member who doesn't mind schlepping through paperwork too much. They might hire a law firm to help.

The estate can be dissolved (effectively, killed as a legal person) and when there is nothing left in it.