The previous answer is not 100% accurate.
What back-end authentication ACTUALLY does is ensure that the public-key your backend server reports (when ELB is talking to your server over HTTPS/SSL) matches a public key you provide. This would prevent somebody from attaching a malicious server to your ELB, or mitigate somebody hijacking the traffic between ELB and your servers.
Back-end authentication does NOT take into account whether or not the client (a browser for example) is communicating to your ELB over HTTPS/SSL. You can have an ELB communicate to a client over HTTP, while communicating to your backend servers over HTTPS/SSL with backend communication. This would only ensure the communication between ELB and your server is secure, NOT if the clients connection is secure.
As long as your ELB is communicating to your backend instance over HTTPS, that traffic is encrypted, although it may be hijacked. Back-end authentication helps prevent that traffic from being hijacked.
Why would you not use back-end authentication?
Performance. With back-end authentication enabled, we've seen around a 50-70ms increase in response time when communicating through ELB (with all other HTTPS is enabled).