Pera pera (ぺらぺら) means fluent: にほんごが ぺらぺらです is “their Japanese is fluent”.
It is the compliment every learner hopes to hear one day — and, in Japan, often hears much sooner than expected.
What it means
ぺらぺら is the sound of pages flipping quickly. Said about a language, it means words come out smoothly and fast, without stopping to think. It also has a second, older meaning: thin and flimsy, like cheap paper.
How to use it
Like ぺこぺこ, it describes a state, so it takes です: にほんごが ぺらぺらです. Put the language before が. You can also put it in front of a verb: ぺらぺら はなします, “speaks fluently”.
ゆきさんは えいごが ぺらぺらですね。
Yuki, your English is so fluent.
いえいえ、まだまだです。
Oh no, I still have a long way to go.
すごいです！
That's amazing!
Close cousins
すらすら is smooth too, but for reading, writing or answering without getting stuck: すらすら よめます, “I can read it easily”. べらべら is the unkind one: someone talking too much, or telling a secret they should have kept. ぺらぺら is the compliment.
In manga and anime
The classic scene is a foreign character who opens their mouth and surprises everyone: ペラペラ！ Watch for the reply, too. The person praised almost always waves it away.
Can you use it?
Yes, as a compliment for someone else. Don't say it about yourself: it sounds like boasting. And be ready to hear it: in Japan, even a short こんにちは can earn a friendly “にほんごが じょうずですね”.