A lot of websites have newsletters or mailing lists, a lot of them are managed by internal systems and many are external.
Sometimes, regardless of whether it seems to be internal or external, when I unsubscribe from a newsletter I'll be told that my request will take "between 2 and 5 days" or "up to 48 hours" to be processed.
Why is this? Surely it's just a matter of deleting an email address from a table. Is it a ploy to keep me subscribing, in the hope that those 48 hours will be enough time for me to realise the mistake that I've made?
What I think is more likely, though, is that they are using a fairly sophisticated email service which is capable of generating millions of emails and queuing them up in advanced of a scheduled delivery date.
Say you had 10 Million subscribers that you wanted to email a coupon or offer to that was only good for the next 24 hours (e.g. "Saturday's 1 Day Sale"). In order to get those into 10 Million inboxes within a 10 minute window you need to pre-process as much as possible. The email marketing person schedules emails to go out at a certain time, they are generated and queued, and then pushed out in bulk. Checking if you've unsubscribed is most efficiently done when generating the emails to be queued, not when going to send.
So when you go to unsubscribe, they might have an email or two in the queue ready to go to you. It's much easier to say it will take 48 hours for your unsubscribe request to go through than it is to explain that "you're unsubscribed, but we might have a few emails in our pending queue that would be a pain for us to delete or prevent from going out, so please just forgive us during this period."
(Side note: There's a surprising amount of interesting tech going on in some, but not all, email marketing programs.)