First, are you executor for both parent's wills? Presumably, they won't die at the same time, so that is important to know.
I would find out if you are sole executor, or if you will share the job with someone else. If shared, you obviously should know who it is so that you can decide if it's someone you can work with.
Where will the wills be kept? At a solicitor's office, in a safe deposit box, or somewhere else? Obviously, you need to know who the solicitor is, where the deposit box is, etc.
Are your parent's estates sizable? Are their financial affairs complicated, or straightforward? Are things in order, or will there be alot of sorting out to do? All this will figure into how much time you will need to spend wrapping things up. Sometimes a family member as executor is entitled to some sort of financial remuneration for the work involved/time spent. If the estate is sizable, this is fair as it will consume alot of time and energy. Obviously, solicitors and banks are paid for their time, or sometimes charge a flat fee (usually a percentage) for work done.
In my experience, being an executor means working with your parent's solicitor (presumable the same person who wrote the will?). You will need to arrange for all debts to be paid, for all bequests to be carried out, and for tax returns to be filed and taxes paid. Whatever is left over will be divided between beneficiares under the terms of the will. Will you have to arrange for a house to be sold? Will the surviving spouse inherit the deceased's assets?
Lots to think about......and you're wise to plan ahead for what you've agreed to.