The Elite Praetorian Guards are a group of unnamed humans garbed in red armor and robes who serve as guards for Supreme Leader Snoke in much the same way that the Emperor's Royal Guards served Emperor Palpatine.
They appear in Star Wars: Episode VIII - The Last Jedi as supporting antagonists.
The guards were presumably created to mirror Emperor Palpatine's Emperor's Royal Guards, as Supreme Leader Snoke's First Order mirrored the Galactic Empire in various ways. The eight Praetorian Guard's origins are not known, nor are any facts or details about just how they were selected or trained for their role. But ultimately, they came into being as Supreme Leader Snoke's personal protectors, being absolutely loyal to him.
This loyalty to Snoke went even into death; after Snoke was betrayed and bisected by his hitherto loyal servant Kylo Ren, the guards immediately turned on him. However, Kylo Ren and the aspiring Jedi Rey worked together to survive and managed to kill all eight of the guards. Once they've all been dealt with, Kylo Ren offered Rey a place to rule the galaxy by his side, but she refused and escaped, and he then took over as the new Supreme Leader of the First Order.
- There being named "First Guard", "Third Guard", "Seventh Guard" and so on brings to mind the similar practice of Emperor Palpatine's Inquisitorius being named a number followed by either "brother" or "sister". This indicates that the Guards may have been inspired by Palpatine's Inquisitors as well as the Emperor's Royal Guard.
- As already noted, they were based on Palpatine's Royal Guards, but designed to look more "combat ready," so instead of wearing ceremonial flowing red robes with armor beneath it, the Praetorian Guards are more visibly armored. Said armor design was inspired by Samurai Armor (coincidentally, Samurai armor also inspired Darth Vader's armor design, and Luke Skywalker's actor Mark Hamill likened the movie the guards appear into the film The Last Samurai).
- They are named after the Praetorian Guards from Ancient Rome and serve a similar function of protecting the designated leader.