Rashbi says in Maseches Shabbos “כל ישראל בני מלכים הם”, “All Yisroel are children of kings,” in looser translation, every Yid is royalty. It says there in regards to a case of financial halocho that if someone who owes a debt can’t pay, and he has a robe that is expensive in relation to the debt, the robe is given up to pay this debt and he is given one that is proper to his station. R’ Akiva says that for all Yidden it is suitable they should wear such a robe.
The word used in Shas for this is “איצטלא”, which in the Hagohos V’Tziyonim on the side of the daf explains to be some sort of robe with a belt. That this is brought up in regards to the concept of Klal Yisroel being descendants of royalty. Considering what it says in the Torah, that Klal Yisroel is to be a kingdom of priests and a holy nation, we can perhaps understand more of the true nature of what R’ Shimon bar Yochai says.
The royalty of Klal Yisroel is not like that of the nations. Rather than our royalty being expressed through gaudy, glitzy, clothes what show off physical figure, our clothes specifically cover the body and remind us to be separate from coarse desire. As is known from the Shulchon Oruch we have to have some form of division between our hearts and lower regions, especially the area of Yesod. Really it is proper the gartel, the belt, should be worn just below the heart and ribs, in order that everything lower than the heart, where our less noble functions of digestion and excretion begin, should be separated. The purpose of this is to serve as a reminder that we should focus on higher things during prayer, rather than being concerned with lower needs. Up until the modern era, the basic clothing of a Jewish man was a long robe-like garment that reached the feet, along with a gartel set in the middle of the body. The only reason the gartel was ever placed around the waist was due to a decree by one of the Russian Czars, and unfortunately this has become the common practice. The royalty of Klal Yisroel is expressed through modesty, and our focus on the Torah and our Father, the King of the World, as we try to say at least 100 times a day through various brochos.
Unfortunately, many seem to have adopted the attitude that being a Ben or Bas Melech means that we have to dress as fancy as possible, have a chandelier in every room, and other such things. This is the complete opposite of what Rashbi means when he says we are all royalty. The fact that Hagohos V’Tziyonim specifically includes there the comment about the belt with a robe serves to remind us that our true royalty comes through modesty and focusing on elevated things, rather than things of this world.