Bo-Katan Kryze's blue Mandalorian armor is noticeably different from what audiences have seen in The Mandalorian so far, and there's a reason behind the color scheme. First appearing in the Clone Wars animated series and then later making a guest appearance in Star Wars Rebels, Bo-Katan quickly became one of the most recognizable Mandalorians in Star Wars canon. Since most of the Mandalorians from the Expanded Universe were de-canonized when Disney purchased Lucasfilm, fans have had to rely on the animated shows for rebuilding that world.
During the prequels era, Bo-Katan fought alongside Pre Vizsla and his Death Watch, a radical faction of Mandalorians who opposed the Duchess of Mandalore - Bo-Katan's sister, Satine Kryze - during the Clone Wars. For some time she and her Nite Owls - an elite unit of Mandalorian warriors - worked with Death Watch, even when Maul took over the group and created the Shadow Collective. She followed Maul up until they took over Mandalore from the Duchess; what changed her allegiance was Maul taking the throne for himself instead of putting Pre Vizsla in charge. And so, Bo-Katan rebelled against Maul and split apart from Death Watch and the Shadow Collective.
In spite of leaving Death Watch behind, Bo-Katan and her Nite Owls remained active; furthermore, their mission never changed, only the leader did. In keeping with their identity, the Nite Owls kept the blue-and-grey color scheme for their armor, which is the same as Death Watch's colors. While Din Djarin's armor uses a basic greyish steel color, many Mandalorians - the most notable being Sabine Wren - have modified their armor to fit them by changing the colors. But the armor itself gets passed down through the generations, as Bo-Katan noted in The Mandalorian.
It's worth noting that the two other Mandalorians who appeared with Bo-Katan in The Mandalorian season 2 also wore blue-and-grey armor. However, only Koska Reeves (Sasha Banks) had an owl design on her helmet, which represented her membership in, and allegiance to, the all-female Nite Owls. Meanwhile, Axe Woves (Simon Kassianides) did not have an owl design on his helmet, even though his armor was also blue-and-grey; the most likely reason for that is because he's a former Death Watch member who sided with Bo-Katan in opposing Maul's leadership.
Over the years it's never been confirmed why exactly Bo-Katan and the Nite Owls actually use owls as their symbol, but in Star Wars, various animals play an integral part in balance and understanding the Force. For example, the owl Morai represented the Daughter and would always follow Ahsoka Tano around, including appearing in the Clone Wars series finale. Given the fact that Mandalorians are a race deeply rooted in tradition, somewhere down the line an owl must have come to represent something close to what Bo-Katan and her Mandalorians stand for.