What is the purpose of minor basilicas? What is the difference between them and a normal cathedral? As far as I can tell its purely ceremonial. If that is true, what aren't all cathedrals designated basilicas? Is it just a tradition to have hierarchy of cathedrals?
A cathedral is the seat of the diocese, where the bishop conducts mass.
Cathedrals are given the precedence of the diocese: more important or influential dioceses have more precedence, with the Diocese of Rome (the seat of the Pope) having the highest precedence. Like getting a particularly influential ambassadorship or corporate title, it's a mark of honor to be assigned to a diocese with higher precedence.
One thing to keep in mind is that there is no higher ecclesiastical rank than bishop: even the Pope is a bishop. But as with most bodies of equals there is a pecking order, as it were: the Bishop of Rome (the Pope) is essentially the first among equals. The precedence of the bishops and their diocese is meant to provide some amount of order and structure to a large number of bishops.
If you're familiar with the United States Senate, another way to look at it is how seniority is established there. Even though they're both duly elected senators, Sen. Chuck Schumer has more seniority and influence than Sen. Kirsten Gillabrand.
A minor basilica is the formal designation of a church that is more notable than regular churches, but does not act as the seat of any bishop.
The purpose of designating a church a minor basilica is the recognize the historic nature and importance of the church; essentially it's an honorific that can be bestowed for a variety of reasons as long as the church has demonstrated its notability or magnificence to the Sacred Congregation of Rites. Robert F. McNamara mentions a few different ways a church can do that:
Because of its notability, minor basilicas have higher precedence than other churches, but they are outside of the cathedral hierarchy: a basilica that is not also a cathedral is not given precedence over a diocese's cathedral.
For the sake of completion, there's also the major basilicas, also known as the Papal basilicas, of which there are four (all in Rome):
These are given the highest precedence, and only the Holy Father and his delegates are allowed to conduct mass in them.
From what I understood during a recent visit to Saint James Cathedral Basilica in Brooklyn, after having read the what was written by the pope saint John Paul II when the Cathedrale it received Basilica status (forgive my ignorance of proper terms)...it's certainly not to make the church more prestigeous, for 'pretiges' sake...but to corroborate an already existing 'aura', a unique and outstanding force and grace associated with the church and to the saint or saints from whom that emerged. The 'purpose'could be defined as being an important recognition of a supernatural charisma, so as to attract more souls and do more good.