Crownsguard is an elite group of soldiers usually tasked with the protection of the royal family of Lucis, the city of Insomnia and the Citadel in Final Fantasy XV, although its focus was changed right before the start of the game.
According to the Final Fantasy XV Ultimania, the Crownsguard's roots lay in the Lucian army that was dissolved 150 years ago when Lucis was isolated from the rets of the world by the monarch's magic barrier. At M.E 606 the Lucian army was dissolved and reorganized into a countermeasure-only defense force, the Crownsguard.
Notable members include Clarus Amicitia, King Regis's "shield" and bodyguard; Gladiolus Amicitia, who serves the same role for Prince Noctis; Ignis Scientia, Noctis's royal adviser who at one point identifies himself as a servant of the Crownsguard; the Crownsguard's commander, Cor Leonis, a legendary soldier known as the "marshal"; and Monica Elshett and Dustin Ackers who help Iris Amicitia escape to Lestallum.
The player party's default attires are provided by the Crownsguard, as is Noctis's smartphone. Cor dresses in a similar manner. At one point, Ignis tells Prompto that in the Crownsguard one's attire identifies them, and asks him to wear it with pride. Crownsguard's insignia appears similar to the one used by the Kingsglaive of a Bahamut with fifteen swords, as it appears on Gladiolus's vest in the "no jacket" version of his default attire, and on the Crownsguard decal for the Regalia.
At the Crownsguard's training hall, Clarus Amicitia tells Gladiolus about the security measures in place during the upcoming signing ceremony of the treaty between Lucis and the Niflheim. Marshal Cor Leonis would be on external patrol that day and the Crownsguard will operate as usual. Only the bare minimum will be on duty, as the Citadel will be left to the Kingsglaive, another elite group working for the royal family whose special trait is that they can channel and use the king's magic.
The peace has brought along many changes, including the role of the Crownsguard, whose new place will be with the people now rather than the king. Clarus doesn't mind as protecting the populace ensures their support for King Regis, as the Amicitia family has but one duty: to safeguard and support the king. Clarus asks Gladiolus to keep Prince Noctis safe, not just as the next king, but as a comrade and a true friend.
Cor arrives with Prompto Argentum, who has arrived for his Crownsguard uniform. Prompto is nervous to be meeting Clarus, and affirms he has completed his self-defense training for the journey. Gladiolus and Prompto leave, and the atmosphere becomes solemn. Cor is unhappy the Crownsguard has been excluded from everything related to the signing, and Clarus reminds him that the new orders are for the Crownsguard to protect the people of Lucis, and says that the Kingsglaive are is the only ones who can fight the Empire if something goes wrong.
Regis knows that the treaty-signing is a ruse, and thus is going to send Noctis away from the city. Clarus is the same, and both feel burdened that they have been unable to tell their children the truth of what is to come.
Insomnia falls and the Empire steals the Crystal from Lucis. King Regis is killed and daemons destroy the city. Cor ushers Noctis to his new quest of reclaiming the kingdom by collecting the royal arms of his forebears and forging covenants with the astrals. Still following his original orders from the late king, Cor concentrates his efforts in helping the people of Lucis. He works with the local hunters and supports Noctis from afar. Gladiolus stays by Noctis's side, more as a friend than a member of the Crownsguard, however.
When Noctis's party meets with Monica Elshett at a prairie outpost, they learn most of the Crownsguard didn't survive Insomnia's invasion. Monica and Dustin Ackers, members of the Crownsguard, had escorted Lady Iris out of the city and Dustin accompanied her the rest of the way to Lestallum. Monica and Dustin later come to stay at Cape Caem with Iris and Talcott Hester.
After Noctis returns after sleeping inside the Crystal for ten years, his friends don the uniforms of the Kingsglaive when they accompany him as he heads to the ruins of Insomnia to fulfill the prophecy as the True King.