When we say "out-of-band exchange of symmetric keys", what does "out-of-band" mean?
Out-of-band is activity outside a defined telecommunications frequency band, or, metaphorically, outside some other kind of activity.
It just means through another means of communication than the one you use to exchange the ciphertexts.
If you are sending the encrypted messages over the internet, calling up the other person on the phone and reading the key to them would be transmitting it "out of band". So would meeting the person IRL and giving them the key or sending it in an ordinary letter.
The point is that you have on (relatively) secure means of communication (where you don't think there is any eavesdropper). You can use this channel to transmit a symmetric key, that you can later use to communicate securely on an insecure channel (where there might be eavesdroppers).