Hanabi means firework, literally the kanji means "fire flower". Taikai means "big meeting" or in this case a "Hanabi Taikai" is a Fireworks Display Festival.

In Japan, Summer is Hanabi Taikai season.  From mid July actually all the way to October there are hundreds of hanabi taikai all around the country.  In Japan the big shows have between 10,000 and 30,000 fireworks and goes for 60 to 90 minutes!!!