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Because printf-style format strings are interpreted at runtime, rather than validated by the Java compiler, they can contain errors that lead to unexpected behavior or runtime errors. This rule statically validates the good behavior of printf-style formats when calling the format(...) methods of java.util.Formatter, java.lang.String, java.io.PrintStream and java.io.PrintWriter classes and the printf(...) methods of java.io.PrintStream or java.io.PrintWriter classes. 
Noncompliant Code Example

String.format("The value of my integer is %d", "Hello World");  // Noncompliant; an 'int' is expected rather than a String
String.format("First {0} and then {1}", "foo", "bar");  //Noncompliant. Looks like there is a confusion with the use of {{java.text.MessageFormat}}, parameters "foo" and "bar" will be simply ignored here
String.format("Duke's Birthday year is %tX", c);  //Noncompliant; X is not a supported time conversion character
String.format("Display %3$d and then %d", 1, 2, 3);   //Noncompliant; the second argument '2' is unused
String.format("Display %0$d and then %d", 1);   //Noncompliant; arguments are numbered starting from 1
String.format("Too many arguments %d and %d", 1, 2, 3);  //Noncompliant; the third argument '3' is unused
String.format("Not enough arguments %d and %d", 1);  //Noncompliant; the second argument is missing
String.format("First Line\n");   //Noncompliant; %n should be used in place of \n to produce the platform-specific line separator
String.format("%< is equals to %d", 2);   //Noncompliant; the argument index '<' refers to the previous format specifier but there isn't one
String.format("Is myObject null ? %b", myObject);   //Noncompliant; when a non-boolean argument is formatted with %b, it prints true for any nonnull value, and false for null. Even if intended, this is misleading. It's better to directly inject the boolean value (myObject == null in this case)
String.format("value is " + value); // Noncompliant
String s = String.format("string without arguments"); // Noncompliant

Compliant Solution

String.format("The value of my integer is %d", 3);
String.format("First %s and then %s", "foo", "bar");
String.format("Duke's Birthday year is %tY", c);
String.format("Display %2$d and then %d", 1, 3);
String.format("Display %1$d and then %d", 1);
String.format("Too many arguments %d %d", 1, 2);
String.format("Not enough arguments %d and %d", 1, 2);
String.format("First Line%n");
String.format("%d is equals to %<", 2);
String.format("Is myObject null ? %b", myObject == null);
String.format("value is %d", value);
String s = "string without arguments";