Wishlists, in the context of digital storefronts, are lists of videogames that you wish somebody would buy for you so you don't have to spend your own money on them. It's a common feature, supported by Steam, GOG, Origin, and even the Windows Store, but for some reason it hasn't been available on the one storefront that's putting the most pressure on Steam—the Epic Games Store.
As of today, that's no longer the case. Fire up the EGS client, or pop around to the store site, and you'll notice that next to the "Buy Now" button on game listings is a new, smaller button with the outline of a heart on it. (You can also see it in the image above.) That's the wishlist button: Click it, the heart will fill in, and the game in question will be added to your wishlist. To view the contents of your wishlist, hit your account menu, at the top of the screen on the EGS website, or down in the bottom-left corner in the launcher.
This "first iteration" of wishlists is fairly basic, but Epic plans to add filtering and smart searches in future updates, as well as email notifications when the status of wishlisted games changes—when they release or go on sale, for instance. If you have other thoughts or feedback on EGS wishlists could use, Epic will be happy to hear about it on Facebook, Twitter, or Instagram.
At the moment, the Epic Games Store Trello—basically a live development roadmap that's open to the public—has wishlists in the "Up Next" category, which also includes an "algorithmically-driven trending category" for the EGS storefront, mod support, and self-serve refunds. Their arrival may not be as imminent as the category title suggests, however: Self-serve refunds was added to "Up Next" in October 2019, while trending and mod support were put there in August.