What does waiving an issuance and services of citation mean when probating a Will?

These terms are not used in Florida, where I practice.  However, it is common in all jurisdictions to ask the people who would be entitled to serve as executor/administrator/personal representative of an estate to waive their right to serve, consent to appointing a specific person, and waive their right to receive formal notice of estate proceedings. 

If you do not care to serve as personal representative of the estate, agree that the named person should serve, and trust the named person and court to handle the estate correctly, then you can safely waive these matters.  If you have concerns about any of this, I suggest you contact the attorney who sent you the waiver and ask any questions you have.  If you are not satisfied with the answers, don't sign it. 

If you do not waive, then you will be notified of hearings or actions in the estate.  If you want to object or be heard about these matters, you will  have to appear in court to do so.  It is best to have a lawyer for this, but you don't have to hire a lawyer.  Failing to sign the waiver will make the estate take longer to complete, so it is best to sign the waiver if you don't have significant objections to anything I mentioned here.