Sense 1. Words come out from a mouth
Meaning 1: “very fluent in a (foreign) language”
In this usage, it is often used as “Xがペラペラ” where X is an arbitrary language, and that means “You’re fluent in X”.
* A lot of Japanese people — mostly due to the inexperience of living abroad — mistakenly believe that once you live in a foreign country, you’ll be fluent in the language of the country without making much effort (that’s not true, of course). Therefore, when they meet some Japanese people who have lived in a foreign country, they often ask them “じゃあ、英語(えいご)ペラペラでしょ？”, meaning “Then, you’re fluent in English, right?”. The definition of “pera pera” varies greatly depending on people; some regard you as “pera pera” if you can manage to have a conversation with someone in the language, while others assume that “pera pera” is equivalent to a native level.
Meaning 2. “talk/gossip about something thoughtlessly”
Sense 2. paper-thin
Meaning 2.1. “paper-thin”
It is often used negatively to describe thin clothes or materials.
Meaning 2.2. “very shallow, airhead”
It is often used negatively and sardonically to describe shallow things that have little meaningful content, or people who have little thoughts or ideas. In this usage, ペラペラ is often written/pronounced as “ペラッペラ”
Meaning 2.3. “Page flip sound”
It is often used as “ペラペラと”.
Turn/Leaf through pages (with “pera pera” sound).