Pika pika (ぴかぴか) means shiny, sparkling clean, or brand new.
You already know half of this word. The “pika” in Pikachu comes from ピカピカ, the sparkle of electricity; “chu” is the squeak of a mouse.
What it means
ぴかぴか is a bright shine: polished shoes, a car just washed, a kitchen after a big clean. Because new things shine, it also means brand new.
How to use it
For the state of something, add です: ぴかぴかです. In front of a noun, join it with の: ぴかぴかの くるま, “a shiny new car”.
あたらしい くつですか。
Are those new shoes?
はい！ ぴかぴかです。
Yes! Nice and shiny.
Close cousins
きらきら is a gentle twinkle of many small lights, like stars or the sea. つるつる is shiny and smooth, so smooth it is slippery: a polished floor, an icy road. ぴかぴか is the bright, clean shine.
In manga and anime
ピカッ is a single flash: lightning, a camera, or a bright idea appearing above someone's head. And of course, ピカピカ is what a certain yellow mouse says.
Can you use it?
Yes, anywhere. Shops, cleaning products and car washes use it all the time. It is cheerful and easy.