With a static method you dont need to have an instance of a class before you can invoke the method. Example JDBCHelper.getConnection(). The class JDBCHelper gets you a database connection through getConnection() and you dont necessarily need a class instance for a method like that.
Non static methods are associated with a class instance. For example...
new Integer("5").getIntValue() and new Integer("4").getIntValue() will retrieve different results since getIntValue() will return a value based on the instance and not based on the class.