Priests have a limited color palette when they go to put on their vestments to celebrate Mass. In general, they have the option of green, violet, red and white (black and rose are two rare colors that are rarely an option).
However, Spain has a particular privilege in wearing vestments that are blue.
According to Gregor Kollmorgen in an article on The New Liturgical Movement, Spain was given the option of wearing blue "by Bl. Pius IX in recognition of Spain's leading role in the propagation of the recently defined dogma."
Furthermore, John Walsh specifies this indult in his book, The Mass and Vestments of the Catholic Church:
Blue vestments by special papal grant are allowed in the dioceses of Spain on the feast and during the octave of the Immaculate Conception and on all Saturdays when a votive Mass of the Blessed Virgin is permitted. On all those days the use of the blue vestments is of obligation.
This special permission was extended to all Spanish territories at the time, which is why places like Mexico have a similar tradition.
In the United States some priests wear vestments that are primarily white, or primarily gold, with some blue on it. These vestments are not considered blue vestments, as the ones Spain is permitted to use are completely blue.
The color blue has a long tradition connected to Our Lady and is featured in many paintings and icons of her.
