I was asked to explain an assent form for the administration of an estate of a deceased person. In the probate process, there are a number of actions of the Executor that require approval by the Judge. Our probate system generally works on the assumption that the parties to the estate have the most knowledge. If the parties (heirs) want to object to the actions of the executor, then the court will look at the actions with more care. Otherwise, the court can assume that everything is proper. So when a judge's approval is requested, the heirs and other parties are given notice of the issue and given an opportunity to approve or object. If all parties approve, it can expedite the process and decrease the cost. If a person objects, it may create an issue for the court to investigate and hold hearings to resolve. The third choice is to do nothing and let the court decide what action to take without guidance from the parties.
If a party is requested to sign an assent, there are documents that will be submitted to the court which explain the proposed action. The first opportunity to assent is to approve the will and appoint the executor. The subsequent assents could be all sorts of things. Nobody should sign an assent unless they have copies of the documents relating to the issue and understand the contents. The assent will identify the document that is submitted to the judge. An assent says to the court that you approve the proposed action of the executor. It also says to the court that you don't need further notice of the proposed action.
The following is an example of how this works. When the probate is filed, the petitioner files a copy of the will with a petition to probate, a death certificate, and a bond. If you sign the assent, you probably won't get further notice of the petition to probate. If you don't sign the assent, you will be "served" (probably by mail but possibly by a sheriff) with a court document called an order of notice that tells you the petition and will were filed and that you are an interested party and have the right to object to the petition. It will also tell you the date by which you must file your objection. If you don't file the objection by that date, you will not have the right to contest the will or appointment.