MySQL Query and Checkbox Approach

I'm not 100% certain what results you want to have returned, but you can get the distinct pno and name for each one that has both Math and Biology with a query like:

SELECT DISTINCT Table1.pno, Table1.name
FROM SomeTable Table1
  INNER JOIN SomeTable Table2 ON Table2.pno = Table1.pno AND Table2.lesson = 'Biology'
WHERE Table1.lesson = 'Math'
ORDER BY Table1.pno

For a more flexible query to support any number of matches, assuming you only ever have one of each lesson type (you may want to do a unique key on pno and lesson to guarantee this), you can do something like:

SELECT pno, name
FROM SomeTable
WHERE lesson IN ({Match List})
GROUP BY pno, name
HAVING COUNT(1) = {Total Number of options}
ORDER BY pno

Where the {Match List} is your list (such as 'Math', 'Biology' in your original question), and where {Total Number of options} is equal to the number of unique values that all have to match (2 in this case). Again, let me stress that this only works if each lesson per pno is unique... the moment it isn't, you'll get false positives.

you may looking for this

$sql="select * from your_table 
where lesson =  '$biology'";
                      ^^-------this is the variable of which they select from check box

and when they select the other checkbox

you may add this

$sql .= "OR lesson= '$math' " ;

If you want the list of people that take both Maths and Biology, this should work:

SELECT t1.pno, t1.name
FROM myTable t1
WHERE EXISTS
(
SELECT 1
FROM myTable t2
WHERE t1.pno = t2.pno
AND t2.lesson = 'Math'
)
AND EXISTS
(
SELECT 1
FROM myTable t3
WHERE t1.pno = t3.pno
AND t3.lesson = 'Biology'
)