As ahundiak has stated, but should offer a little explanation as to understand what happens with PHP:
In case of check boxes, the only way to to get multiple values back is to add brackets, [], the end of the name property of the check box tag. When the form is submited to a PHP script, it will see the brackets and say "Oh, that is an array!" and will store all the values accordingly.
Now this does produce a small problem if you want to use Javascript to do something with said check boxes, but can be handled reasonably well.