Three is a Magic (Items) Number
Attuning to the Magic
What Does This Mean?
Attuned or Not Attuned?
If you have an item that requires attunement and you do not do the proper time needed to bond with said equipment, your character only gains the nonmagical benefits. That means if you have a really cool Holy Avenger Longsword and forget to attune when you come to battle it acts like a plain longsword. Usually a short rest is required for the attunement process to be complete, which can be a great opportunity for potential role play. DM's can encourage players to act out them trying out the new magical weapon, putting on a fashion show to see how new cloaks or armor looks, etc. rather than a player saying that they sat with it for a short rest and they're attuned.
There are ways to become unattuned to things as well. Rules as written state: "A creature’s attunement to an item ends if the creature no longer satisfies the prerequisites for attunement, if the item has been more than 100 feet away for at least 24 hours, if the creature dies, or if another creature attunes to the item. A creature can also voluntarily end attunement by spending another short rest focused on the item, unless the item is cursed. " Read more rules as written in your Wizards of the Coast Manual or on D&D Beyond.
What I love about this rule as written is the section of the player dying. Players don't always realize that once their player goes down, their attunements end, making it even more of a deterrent for players to not go straight back to the front lines after such a traumatic event.
After some consideration I really enjoy the fact that there are only three attunements for each player available. At my tables I see a lot more sharing of magic items, and being overall more grateful when things show up in game. Magic is supposed to be special, which is lost in fantasy game. This rule brings back the awe that comes with discovering something cool, and having the true conversation between players of who needs this item/would most benefit from it. There is less power grabbing with three attunement item slots and I don't see players trying to stockpile as many magical items as they can.
As a DM I have been able to see players grow and see the true potential of different classes because they are no longer focused on what magic items they have to fix all their problems. Granted, there are a lot of magical items available that do not require attunement, and shops still sell scroll/potions to help non casters. Over all the table has done well with this new rule with Fifth Edition.