What is Form un/subscription?
Form subscription means the subscriber enters his/her details into a form and click on 'Subscribe' button to get subscribed.
Form unsubscription means the subscriber enters his/her details into a form and click on 'Unsubscribe' button to get out of your list.
You will setup a subscription form on your site so your visitors enter details into the form and subscribes into your list. Some forms are capable of unsubscription by offering an option to unsubscribe.

What is Email un/subscription?
Email subscription means the subscriber sends an email to your autoresponder program to get subscribed.
Email unsubscription means the subscriber sends an email to your autoresponder program to get out of your list.

The person clicks on email link that looks like in the above image. So their default email client (mostly Microsoft outlook) opens up and the person can send an empty email to your script to get subscribed. Sameway if a person clicks on unsubscribe email link, default program opens up with 'Unsubscribe' in subject line. If the person sends this email with subject line 'Unsubscribe' to your software, he/she will be unsubscribed.
To process email un/subscriptions, your autoresponder software should be equipped with it and your server should support email piping.