The basis of Tomodachi Life is this. You're the omnipotent (kinda) mayor of a little island and you help manage the life of the Miis who live there. You can create them, import them or get them via streetpass.
Finally, something that can actually use your Miis in the Mii plaza for something useful. However, unlike the Sims you don't actually have total control of your Miis. Instead, your Miis will have their own personality which will cause them to act in different ways. At most you can try to subtly influence them to perform certain things but this isn't likely to work. It's like an even more indirect version of Majesty; the PC Strategy game. This has both its good and bad points. The bad being that obviously you can't control your own Miis, hence you can't sate that god-sim desire within you. However, the good is that IMO it makes the games playability last longer. I got bored of Sims 1-3 after a while because I could just make everything go my way as long as I could be bothered to micromanage. However, no such luck in this.
So really, all you do is take care of their basic needs like food, dress them up however you want and then help them with their little problems and play games with them. They're almost like children but without the constant need to take care of them all the time.
What's great about the game? In all honesty, this IS pretty hard to define. Tomodachi life is probably one of those games you will either love or hate, depending on the type of person you are. However, if you DO like Sims and Animal Crossing, chances are you will like Tomodachi Life.
I've also got to hand it to the creators of the game. This game has some pretty weird sequences in it. Like 80s cartoon weird. Like shrooms weird. In fact, I suspect some of the sequences were written while the creators were on shrooms. That's just part of the quirky charm of the game.
So in the end, I can't really say Tomodachi life is a great game. I found it interesting enough to try and buy it on day 1 after all, but my tastes are somewhat strange (I didn't like Pacific Rim...). But of course, what is a post about Tomodachi life without an obligatory post with my Mii in it, saying "ADD ME!!"