Assuming that you have used POST
method for form submission, you can do something like this:
html:
<input type="checkbox" name="values[]" value="val1">
<input type="checkbox" name="values[]" value="val2">
<input type="checkbox" name="values[]" value="val3">
php:
if(isset($_POST['values'])) {
foreach($_POST['values'] as $checked){
mysqli_query("insert into tablename(value) values($checked)");
}
}else{
// use Delete query
}