An alias declaration inside a lib declares a C typedef:
lib X
  alias MyInt = Int32
end
Now Int32 and MyInt are interchangeable:
lib X
  alias MyInt = Int32
  fun some_fun(value : MyInt)
end
X.some_fun 1 # OK
An alias is most useful to avoid writing long types over and over, but also to declare a type based on compile-time flags:
lib C
  ifdef x86_64
    alias SizeT = Int64
  else
    alias SizeT = Int32
  end
  fun memcmp(p1 : Void*, p2 : Void*, size : C::SizeT) : Int32
end
Refer to the type grammar for the notation used in alias types.