== compares content of variables. (You know this very well from intA == intB.)
A String variable contains a reference to a String object, so == will compare references.
After
String str1 = "Hi there";
String str2 = new String("Hi there");
str1 and str2 will refer to different string objects, thus contain different references, so str1 == str2 will yield false.
str1.equals(str2) on the other hand will compare the objects that str1 and str2 refers to, which, as you have noted, yields true.
