A Mandalorian is an individual that follows a code called the Resol'nare. The only rule to become a Mandalorian is to follow that code, to speak the language, and to wear the armor. It doesn't matter what your past was, upon becoming Mandalorian that is only moot. The past doesn't matter as much to the Mando'a, only the present and the future. That's not to say they forget the past, quite the opposite. There is a saying that states that Mandalorians have long memories, something that is true. They won't easily forget or forgive a slight against their honor. However, a Mandalorian learns from the past though, and seeks to not repeat any mistakes made prior.
As a whole, the Mandalorian culture has survived since before the formation of the Republic, Jedi, or Sith. Originating from Coruscant and the Taung, they eventually left the planet and traveled to a different planet. That planet became Mandalore, the new homeplanet of the Mandalorians. The Taung were a warrior culture and that transferred to their new culture. Alongside this, family is everything to the Mando'a, and every Mandalorian is "vode" or family.
Mandalorians value family and strength and the defeat of their enemies. To do so, they have absorbed hundreds, if not thousands, of different cultures and modified it to suit themselves, while also modifying themselves. They have kept true to their past though, despite all the wars they have fought. As such, the Mandos value strategy in their campaigns and wars, even if it doesn't seem like it often. However, rank structure is very loose, and very fluid in the battlefield. It's not unheard of for young kids to take command if they know strategy better, as such there isn't a definitive structure to Mandalorian command. There are some consistencies though.
The Mand'alor is at the very top, acting as the leader of all Mandalorians, and their representative. Below said leader are the Alor council, or the clan leaders who act as advisors to the Mand'alor. They have arguably more power than the Mand'alor, but that's a whole different topic. Below the council are the Alors, or clan leaders. And below them come the regular Mandalorians. Ranking structure is tricky though, seeing as in wars it can change, as well as in peace. Same goes for different clans, one clan may have something rigid while the next has something that doesn't even represent a structure, but still works for them. Along side all those listed just now, there are war masters and battlemasters. These take more roles during battles and wars, and pass on information to those below them. Those who achieve these ranks are usually regarded highly, for to get such a rank is to be very skilled in multiple different areas.
Going along the skill talk, Mandalorians value individual skill as much as they value the skill of the collective. As such, those who have a skill usually teach others that skill who then also teach others. Eventually this keeps spreading until a majority have learned this skill, or at least know how to emulate it. Thanks to this, the Mandalorians believe themselves superior, for many skill they know are deadly against their foes, specifically Jedi and Sith.
All in all, the Mandalorians think their culture is superior because of various different reasons. Mainly the many, many wars fought and won by the Mandalorians. They don't force their culture onto anyone, but do allow anyone who wishes to join access to their culture. It's not uncommon for attacked populations to have many younger men and women join the ranks of the Mandalorians upon seeing their strength. This coupled with the adoption of war orphans on planets conquered by the Mandalorians leaves no shortage of soldiers the Mando'ade can use.
To conclude, Mandalorians are a very diverse culture that views itself as being superior to every other culture. They are a warrior society that values family and honor, and will go to great lengths to fight those they view as dishonorable.Mandalorians accept anyone who wishes to join them into their society, it could be a war orphan or a soldier, a man or a woman, it doesn't matter. To be a Mandalorian is to wear the armor, follow the code, and fight for family and Mandalore. They care less about the past and more about the present and future, but still remember the past. Continuing with that, family matters a lot to them, as well as honor. However, there are many different interpretations of that, and this doesn't prevent different Mandalorians from taking up questionable jobs such as piracy. Mandalorians are as diverse as they are unique, and will usually support one another against a common foe, even if they would fight each other in any other situation.
I know it's long, sorry, hehe. Got a bit carried away since I love the Mandalorians so much. I do hope this has helped, I know some of it has been covered already, but still, different take I hope, and some more info.