What does this mean?

select to_date('&1', 'MM/DD/YYYY') into v_start_date from dual;
select (to_date('&2', 'MM/DD/YYYY')+1) into v_end_date from dual;

I am mainly asking about the:

select to_date('&1',

What does the '&1' mean?

The '&1' is an input parameter to your SQL statement. The '1' is the varable name and the '&' tells SQL that the 1 is a input variable.