Freshmen programmer, not quite getting the purpose of initializers and instances in Swift. I need a basic understanding.

When you create an object, all its properties must have an initial value (the exception are Optional types). You can assign an initial value in two ways: direct assign at declaration or with an initializer (init).

class Foo {
  var bar: Int = 0 // direct assign
}

In this example the class Foo has one property initialized directly, but lets say you don't have a sensible initial value and you need to receive that value from somewhere else, you create an init method:

class Foo {
  var bar: Int
  init(bar: Int) {
    self.bar = bar
  }
}

The init method receives an int as a parameter, and assigns this parameter to the bar property (the word self refers to the property, otherwise it would be an ambiguous assignment).

TL:DR; The purpose of init is provide initial values for all the properties, to create an instance in a consistent state