What is the difference between & and &&?

Both & and && is used in a query in order to substitute variables.
"&" is used to create a temporary substitution variable that will prompt you for a value every time it is referenced. Example:

SQL> select * from test where b='&Country_name';
Enter value for country_name: USA
old   1: select * from test where b='&Country_name'
new   1: select * from test where b='USA'

         A B
---------- ----------
         1 USA
SQL> /
Enter value for country_name: INDIA
old   1: select * from test where b='&Country_name'
new   1: select * from test where b='INDIA'

         A B
---------- ----------
         2 INDIA

"&&" is used to create a permanent substitution variable. Once you have entered a value (defined the variable) its value will used every time the variable is referenced. Example:

SQL>  select * from test where b='&&Country_name';
Enter value for country_name: INDIA
old   1:  select * from test where b='&&Country_name'
new   1:  select * from test where b='INDIA'

         A B
---------- ----------
         2 INDIA
SQL>  select * from test where b='&&Country_name';
old   1:  select * from test where b='&&Country_name'
new   1:  select * from test where b='INDIA'

         A B
---------- ----------
         2 INDIA

SQL> /
old   1:  select * from test where b='&&Country_name'
new   1:  select * from test where b='INDIA'

         A B
---------- ----------
         2 INDIA

As we see subsequent run does not prompt for to provide country name if you use && and once we provide value.

The "&&" will actually define the variable similarly to what the DEFINE command does.

If we now invoke define command it will return output as,
SQL> define
DEFINE COUNTRY_NAME = "INDIA" (CHAR)

In stead of && we can also use DEFINE to define a variable like,

SQL> DEFINE COUNTRY_NAME    = "USA"
SQL> select * from test where b='&&Country_name'
  2  ;
old   1: select * from test where b='&&Country_name'
new   1: select * from test where b='USA'

         A B
---------- ----------
         1 USA