Invokespecial used in 3 cases: call to super method, call to constructor, and call to private methods.

InvokeSpecial.java

class A {
  public void superMethod() {}
}

public class InvokeSpecial extends A {
  // Implicit super constructor call - invokespecial
  private byte b = 0;
  { // instance initializer - invokespecial
    b = 1;
  }
  public InvokeSpecial() {} // invokespecial
  @Override public void superMethod() {
    super.superMethod(); // invokespecial
    somePrivate(); // invokespecial
    new String("foo"); // calling String constructor by invokespecial
  }

  private void somePrivate() {}
}

//Compiled from "InvokeSpecial.java"
//public class InvokeSpecial extends A {
//  public InvokeSpecial();
//    Code:
//       0: aload_0       
//       1: invokespecial #1                  // Method A."<init>":()V
//       4: aload_0       
//       5: iconst_0      
//       6: putfield      #2                  // Field b:B
//       9: aload_0       
//      10: iconst_1      
//      11: putfield      #2                  // Field b:B
//      14: return        
//
//  public void superMethod();
//    Code:
//       0: aload_0       
//       1: invokespecial #3                  // Method A.superMethod:()V
//       4: aload_0       
//       5: invokespecial #4                  // Method somePrivate:()V
//       8: new           #5                  // class java/lang/String
//      11: dup           
//      12: ldc           #6                  // String foo
//      14: invokespecial #7                  // Method java/lang/String."<init>":(Ljava/lang/String;)V
//      17: pop           
//      18: return        
//}