“For the holy service is incumbent on them; they shall carry with the shoulder!” (Bamidbar 7:9)
It is a positive commandment that the priests are commanded to carry the Ark of the covenant on their shoulders when they carry it from one place to the next, as it says “For the holy service is incumbent on them; they shall carry with the shoulder!”. This commandment is incumbent on priests and Levites, as they carry the ark.
Amongst the roots of the commandment is that the main honor of Klal Yisrael is the Torah, for by it they are separated from the other nations and made into a part of Hashem. It is therefore fitting and correct to carry it on the shoulders of the most respected and holy members of the nation. There is no necessity to explain this at length as even young children should understand this. The verse itself describes the details of this commandment, which consist of the fact that they must carry it on their shoulders when they carry it from one place to the next, or in times of war etc. and it should not be carried in a wagon or on an animal’s back.
This commandment applies when Klal Yisrael are on their land, as then they were obligated to carry the ark from time to time for wars or at the king’s command. Nowadays, however, due to our great sins, we have no ark and no king. This commandment is incumbent on the tribe of Levi, and on the rest of the nation that they should allow them to perform it.
(The custom that when going out to greet non-Jewish kings the priests and Levites carry the Torah scrolls has no connection to this commandment, as any member of our nation may carry a Torah scroll. If for the honor of the Torah they choose that today members of the tribe of Levi will also carry the Torah, they will receive blessings.)