Which characteristic is given by the principal quantum number?

The principal quantum number, identified by n, gives information about the orbital energy level of the electron.

To understand it better:

According to the current model of the atom, it has a central nucleus with electrons orbiting around. These orbits are located at different energy levels that are related to the distance from the electron to the nucleus.

So, the first energy level, is considered the lowest, because it is the smallest and the one that is in average closer to the nucleus, and as n increases, the farther away from the nucleus is the orbital and therefore more energy the electron has.

It should be noted that the values of n will always be positive integer numbers, for example: 1, 2, 3, 4, 5, 6,7. Although theoretically its value oscillates between 1 and infinity, until now only atoms whose maximum energetic level is 8 are known.

it is a negative acceleration