Sometimes when I take material from time series to study, it appears out of nowhere "for a process to be stationary it is necessary for the roots of the characteristic polynomial to fall outside the unitary circle". Something similar occurs with invertibility.

I would like to know the real importance of these concepts, since the way they are presented, at least in the materials I consulted, they are vague means. From what I've understood so far, stationarity is important because I guarantee constant mean and variance and some models use these assumptions. Invertibility, on the other hand, is the fact that you can write a process, AR (p) for example, in the form of another, $MA(\infty)$.