.equlas() method is in Object class which compares two 
objects and returns true if both are same.

== compares whether two references  pointing to same memory 
location.

== operator return true if both reference variable pointing 
to same object.
equals() method also use == as default, but String and 
Wrapper classes override (you can also override) it but 
meaningfull comparison , as in two same String case it 
returns true for equals()method.

for knowing it clearly make small programs by using both. 
there are so many exception  in wrapper classes.

equals() method is used for comparison. it copares the 
content whereas == is used to compare the references. 

if the hashcode value is same for two objects equals() 
method will return true. but in case of == it is not the 
case.

Try following code 

String str="Java";
String str1="Ja";
String str2="va";
String str3=str1+str2;
String str4 = new String("Java");
String str5 = str4;
String str6 = new String("Programming");
String str7 = new String(str6);
System.out.println(str3);
System.out.println("str "+str.hashCode());

System.out.println("str3 :- "+str3.hashCode());
System.out.println("str4 :- "+str4.hashCode());
System.out.println("str5 :- "+str5.hashCode());
System.out.println("str6 :- "+str4.hashCode());
System.out.println("str7 :- "+str5.hashCode());


if(str==str3)
	System.out.println("str and str3 are equal(==)");
else
	System.out.println("str and str3 are not equals
(==)");
if(str.equals(str3))
	System.out.println("str and str3 are equals(.equals
())");
else
	System.out.println("str and str3 are not equals
(.equals())");


if(str4==str5)
	System.out.println("str4 and str5 are equal(==)");
else
	System.out.println("str4 and str5 are not equals
(==)");
if(str.equals(str3))
	System.out.println("equals");
else
	System.out.println("not equals");


if(str6==str7)
	System.out.println("str6 and str7 are equal(==)");
else
	System.out.println("str6 and str7 are not equals
(==)");
if(str.equals(str3))
	System.out.println("equals");
else
	System.out.println("not equals");