Attestations helps exemplify some scenarios. Alice attesting to something of Bob, can be carried off-chain by Bob and presented when required. Alice can optionally store a hash of the attestation on-chain. But to revoke an attestation, that would have to be stored on chain (or at least a hash of it), and those checking Bob's attestation would have to check on-chain if it was revoked by Alice.
Gaming and advertising examples help explain use cases of payment-channels/side-chains. Eg, Raiden for broadcast-like subscription/payments, or micro-Raiden for game-sessions between participants.