What they're claiming is that your data gets encrypted on your phone and doesn't get decrypted until the intended recipient gets it. Encrypted data can't be read without decrypting it first, so in principle end-to-end encryption ought to keep the app developer from sitting in the middle of your conversation reading your messages.

In reality, though, it's important to remember that anyone can claim their app uses end-to-end encryption, whether or not it actually does. So you shouldn't rely on an app to do the right thing.