It looks as though the Walt Disney World Reservation system is currently experiencing technical difficulties.
When you visit the Walt Disney World website on a laptop or computer, the entire page is having trouble loading. And if you are able to get to the point of clicking on “dining reservations” the page does not load.
When you go onto the My Disney Experience app, a notification instantly pops up that reads “Pardon the Inconvenience: Some of our digital experiences may be unavailable at this time. We’re actively working to resolve this issue. We apologize for any inconvenience.”
Related: Technical Difficulties Allow Crowd to Enter Magic Kingdom Without Scanning Tickets

It looks as though you can still see any current reservations that you may have booked in the past in your My Disney Experience account, but at this moment you cannot currently access the reservation system to book a new reservation.
When trying to call the Disney Dining Reservations line, due to higher than normal call volume (most likely because of the system experiencing issues), the call wait time is over an hour.
Related: Disney app now preferred home for Disney World dining reservations

This is an ongoing issue and Inside the Magic will continue to update you as we gain new information.
More About Dining Reservations
Walt Disney World Resort has several different dining locations for guests to choose from at all four of their theme parks, their two water parks, Disney Springs, and several of Disney Resorts.
Guests can book their dining reservations directly through the My Disney Experience app or online at the official Walt Disney World website.
Guests can also call WDW-DINE, but Disney has previously announced that their preferred method to book dining is on the My Disney Experience app or online at the official Walt Disney World website.