let a = MyStruct(x: 1, y: 2)
  let b = a // Creates a copy of `a`
  b.x = 3 // Won't compile because you used "let", so its properties are immutable
  var c = a
  c.x = 3
  println(a.x) // Prints "1"; the original instance doesn't get changed

  let d = MyClass(x: 1, y: 2)
  let e = d // Refers to the same object as `d`
  e.x = 3 // Allowed, even though you used "let"
  println(d.x) // Prints "3"

That's a basic illustration of the difference between value types and reference types, but there are other differences between structs and classes as well (for instance, structs don't support inheritance or deinitializers).

It comes down to equality. Values have "extensional equality" which means that values A and B are equal exactly and only when they look the same and can be used in the same way. On the other hand, most people are used to "referential equality" which is more strict. It lets me distinguish "your copy" of A from "my copy" of A via their names.

Without referential equality things like mutation fail to have any sense, but programs are in general simpler.