I suspect you and the lady Ts would love it.
My wife has had a blast with it (when it works), and she's never played a pokémon game in her life (though she has seen bits of the TV show and is familiar enough with the concepts and popular characters).
However! You should probably wait until next
weekend with the hopes that they will have straightened out some of the problems by then. Right now it's an infuriatingly broken mess due to its popularity and inability to keep up.
Here's the premise:
You are a pokémon trainer! Your job is (surprise) to catch and train pokémon. You find pokémon by walking around in the real world; this is an augmented-reality game that uses the GPS, gyroscope, and (optionally) outward-facing camera to put you in the game.
Pokémon appear pseudo-randomly (more frequent in some types of areas than others), and when you encounter one, the screen goes from a Maps.app-like overhead view to a camera-perspective view with the pokémon somewhere near you. You throw pokéballs, and if you time one right and are lucky, you catch the pokémon and carry her with you.
Unlike the Game Boy/DS series, there's no fighting with random encounters. Instead, you just try to catch them without wearing them down first. Instead of fighting random encounters to level up your pokémon, you "transfer" (read: sell) your extra pokémon back to the game for points you can use to level up the ones you've kept.
It's a free-to-play game with in-game purchases for extra pokéballs and other items. If you walk around parks, libraries, churches, schools, and other public facilities, you'll very likely find a "pokéstop" which is a persistent totem that you can touch to get extra balls and stuff without having to buy them. They have about a 5 minute cool-off before they refill and you can take items out again. They are only limited per-person, not globally. So, if you and I are standing at the same one, we can both take items at the same time.
Once you start collecting and leveling up your pokémon, you can go to a gym to asynchronously challenge other players. The first one there gets to claim the gym and leave a pokémon behind. If a challenger defeats the pokémon in the gym, she gets to claim it for herself and leave one of hers behind. Rather than "every man for himself" there are three teams everyone joins: red, yellow, and blue. This adds another dynamic to the gym stuff, but I won't get into those details here because I haven't mastered that yet.
This is what the overhead view looks like when you're walking around. You can pinch-zoom and rotate around. That big floaty tower thing is a gym. Like the pokéstops, gyms are persistent at notable locations like churches, parks, etc; that one is at a nearby neighborhood church. I have to be standing in the parking spaces nearest the building to be considered "close enough" to interact with it.
Those smaller floating blue things are the pokéstops that you can visit for free items. There are lots of those things in places around our public parks.