It's simple, it's big, it's mini. It's quite a bang.
To start, you go through levels in which you use fireworks to destroy random stuff on the top screen. Using your trusty stylus, you "sling" on the touch screen fireworks to the top in hopes of destroying them and collecting stars (What's with games and star collecting?...). Sounds simple right? A little, all at the same you're protecting a random object, a ball, a square, whatever. Whatever happens, the sparks from the fireworks that fall must not touch this object, nor should enemy projectiles. In a sense it's like a top down shooter with the objective is to collect stars.
Each stage adds something new, there are 10 levels in each stage, all ending with a boss fight of some sort. While it's intuitive idea of using fireworks as a weapon is good, it lacks any real motivation to play beyond the first few levels. It's a game where it's fun to simply play in bursts of moments, however trying to get too deep into it isn't very fun. It's simple, and that's all there is to it. Nothing more, nothing less.
The stylus as well can create other things such as a "swirl" motion can create a black hole that'll suck in all falling projectiles into it rendering your object safe from harm.
Overall, Big Bang Mini has a good arcade feel to it, simple, good presentation and good use of the stylus however doesn't take you much beyond that and that's it's major downfall.