The first time you hear "This is the way" on The Mandalorian, you're probably wondering what it means. The repeated phrase gets some serious airtime when the still-unnamed hero of the show encounters a group of his own exiled people, and although we don't get the exact meaning or history of the phrase, the context makes it clear why it matters.
We first hear this important new line when the title character is underground with other Mandalorians, getting a new piece of armor made from Beskar steel. A woman questions him, "Have you ever removed you helmet? Has it ever been removed by others?" After he answers no to both questions, she says, "This is the way," and is then echoed by the others present. The line returns again later, when the Mandalorians return to help him get away from the Client's new goons. Our Mandalorian comments, wryly, that they'll need to find a new hideout, and one of his new allies responds again with, "This is the way." This time, the Mandalorian echoes it back as well, the first time we've heard him say it on screen.
Judging by this context, it seems like this is some sort of specifically Mandalorian mantra, perhaps as a reference to preserving their "way" of life. That "way" includes this life of hiding out and living underground, of holding a grudge against the Empire for what it did to their planet and their people, and, apparently, sticking together at all costs. The phrase serves as a connection of sorts, reminding them what they have in common even now.
As we know, this isn't the first time that Star Wars has used some sort of a shared phrase or mantra. The original, of course, is the iconic "May the Force be with you" from the original trilogy of films. In Rogue One, there's a similar mantra repeated by Chirrut Îmwe, a blind Guardian of the Whills: "I am one with the Force; the Force is with me." And, most recently, The Mandalorian has Kuiil, who constantly ends his statements with "I have spoken." In this context, we can see that "this is the way" is more than a catchphrase: it's a revelation of a way of life.
By the time we catch up with the Mandalorians who are shown in the TV series, they've already been through a lot. Mandalore suffered at the hands of the Empire, including something called the "Great Purge," which we can assume was some sort of genocidal event perpetrated on the Mandalorians by the Empire, perhaps as punishment for their continued rebellion and unwillingness to fall in line. As a result, they mostly live underground, rarely emerging, and they stick to a very specific set of rules and guidelines for living — their "way" of life that is all they have left.