The Fallout series are games in a unique setting. You're on a version of earth where, after World War 2, the 1950s style of science fiction came true, then in that world's future, World War 3 happened. The games are set a few hundred years after this version of WW3, among the radioactive remains of that retro-futuristic society. There's also an element of humor in most of the games (4 doesn't seem as funny so far).
It's an open world game. You play either a man or a woman searching for your kidnapped child. While you're following that story, you meet other survivors who offer you quests that you can accept if you want. There's a lot of stuff happening in the world that's not related to you, if you choose to stick your nose in other people's business. You can play it all in any order you want.
The game lets you play in a variety of ways. You can be a badass with a sword, a sneaky hacker who turns enemy robots against their masters, a cold sniper, a charming rogue who can talk your way out of problems, a tinkerer who crafts weapons out of junk you find laying around, etc.
You get to create your own cha racer and get to explore a post-apocalyptic world. There's lots of quests, locations to explore, weapons, and things to collect. Also there's different endings based on your choices.
You're in a post-apocalyptic world and the storyline for each game differs. It's a big exploring and fighting game with multiple quests to do besides the main one and collectibles so there's a wide variety of things to do. I've played the third one before, it's pretty fun.
It's not "suddenly" popular. I'm one of the people who waited for it to come out for years. Fallout is a great and famous series. AzureGirl has already described the setting, so not going to repeat it.