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 will sound to you like gibberish.
To gibber or jabber is to talk rapidly and excitedly without making any sense. Gibberish, ending in -ish like Spanish or English––is the name of the "language" people who gibber and jabber are speaking. It also applies to writing. If you have really bad handwriting, your teacher might say you write in gibberish.