A constructor is a special method in a class that automatically invokes when an instance is created, sharing the same name as the class. There are various types of constructors, including default, parameterless, parameterized, copy, private, and static, each serving distinct purposes like object initialization and memory allocation. A class must have at least one constructor, and a static constructor is unique as it initializes static fields and can only be invoked once per class, with no parameters allowed.