It is about increasing the chance of the user having a look at the popup.

Task completion mode

Users in task-completion mode are eager to fulfil their goal (eg, "Is the product/information/answer I'm after on this page?"). As such, they simply ignore anything irrelevant because it is an obstacle in the way to their goal.

Obstacle placement

On-load pop-ups are typically dismissed because they show at the worse time possible - just when the user can start the journey to her goal.

Delaying the pop-up means some degree of progress towards the goal has been made (partial resolution if you wish); so users are less likely to dismiss the pop-up.

Another strategy you may see is pop-ups that only show when you have reached the bottom of the page. At this point, you can make an assumption that the user has already concluded the relevancy of the page (full resolution) thus a pop-up is not quite an obstacle as it would be at the start or shortly after.

I guess when sites include such popups, on behalf of good user experience, it's because they achieve their goals, which are probably lined up with subscriptions. The users that stay know that there is a subscription letter.

Even if most users go away at first, some stay and some subscribe. So it might be good for their goals to get few subscriptions although they loose most users, which might not be potential subscribers anyway.

They want you to subscribe.

Because subscriptions or email marketing gives pretty nice return on investment (ROI) most of the web admins use extreme measures to capture users attention to users can potentially subscribe.

Pop ups work well for increasing email subscriptions

They may be annoying but surprisingly, they work very well specifically for gathering email subscribers. There is a huge controversy on how to best pitch your users to subscribe to a newsletter. Whether the popup should be displayed when the visitor enters the site, or when she leave's it, or when n amount of seconds has passed. The important thing is to display it at the right time when users are more likely to subscribe on your particular site. The best thing to do is do user tests and try to identify when users are most pleased with your site/app and then fire the pop-up.