When you set up a new subscriber list, people who join it or leave it will by default be shown a very basic unbranded confirmation message, to let them know that their action has been received.
Those are the same for every list, and it isn't possible to edit them at all. However, if you'd like to have more control, you can instead have people redirected transparently to your own site, where you can show your own confirmation pages.
Setting a custom subscribe confirmation page
Jump into your 'Advanced Settings' tab from the Settings Panel, and select 'Subscriber Form'. Scroll down to "Step 4". There you will see the option to enter a URL, under the heading 'Subscribe Confirmation Page (optional)'.
Once you save that change, each new subscriber will be added to your list, and then sent directly to that URL. That gives you the chance to completely control the design, and also to include some useful links or information, so you don't lose them from your site.
Setting a custom unsubscribe confirmation page
Again, start on the Settings Panel and head to the 'Advanced Settings' tab. This time, select 'Unsubscribe Options' on the next screen. On this page, you'll need to enter the URL under 'Redirect unsubscribers to your own confirmation page'.
You can specify up to (3) three different redirect pages and specify which one you want to use on a campaign-by-campaign basis from "Step 1" of the campaign creation process.
Now when people unsubscribe, they will end up on your own page where you can thank them, and perhaps give them the chance to connect with you in other ways.