Edit my application previously selected item should be viewed?

With so little code, it's hard to tell what you actually mean.
I guess you want to repopulate the form with previously made choices if the form isn't filled in completely, right?
Use the form_validation library. It is well documented on the CI website.
There's a function called set_checkbox() in the form helper too.

Code:

<?php foreach($getcert as $student){

Code:

<input type="checkbox" id="mycheck1" name="certid[]" 
       value="<?php echo set_checkbox($student['certid']) ? '1' : $student['certid'] ?>"
        class="cbx">

Code:

output
*********
Array
(
   [id] => 1
   [certificate_id] => 1
   [fee] => 500
   [APPNO] => 10001
   [regno] => 01107402042
   [certid] => 1
   [noc] => 2
   [paid] => 5000
)