Prime delivery day is awesome, especially sharing the same house with someone that orders excessively. We tend to order things throughout the week, then have to deal with a mountain of shipping waste. Prime delivery day condenses the orders as best possible. It's not like I need every single item within 24 hours...
Somewhat tangential, but can't help sharing: It's counter-intuitive, but you should feel good ordering things with same-day delivery, even if you don't need it and it "feels" wasteful. Energy-intensity of delivery basically boils down to "did it go on an airplane?". If so, it has a ton of emissions associated with it. If not, it doesn't. And (of course) the less distance the item has to travel, the less emissions. If it can be delivered same-day, then it's not going on an airplane, and it's not traveling very far.
One weird thing is that it seems like they play a bit fast and loose with the actual meaning of this. Several times I've ordered for "Prime day" because I didn't care and then later got a notification because they just shipped it early anyways. No real complaint per se, but it was still odd.
You need to have Prime, and it usually requires you to have 2-3 items in your cart.
But if they're items that would normally ship in 1-2 days, then it will provide a credits option if you have an Amazon Day (day of the week for combined deliveries) selected and that Amazon Day is at least 3 days in the future. It will also sometimes instead show a "no-rush shipping" option that is usually something like 5-7 days out, with credits.
I'm not going to lie, I almost always select it (even constantly changing my Amazon Day to be at least 3 days out from today), and I'm pretty sure I make back my Prime membership fee and then some. The credits are usually $1.50-$4.50 per shipment, expire after 3 months, and can only be used for digital purchases like Kindle and videos.