Gibberish is nonsense sounds or writing. A baby's babble is often called gibberish. When someone is speaking a foreign language you don't understand, what they're saying may sound like gibberish to you.
To gibber or jabber is to talk rapidly and excitedly without making any sense. Gibberish, ending in -ish like Spanish or English — is the "language" of people who gibber and jabber. The word also applies to writing — if you have really bad handwriting, your teacher might say you write in gibberish. And if your teacher can somehow read your handwriting but your essay is poorly organized, the content of your writing can be called gibberish as well.