With Continuity you can relay your SMS/MMS and calls from your iPhone to your iPad or Mac. That means, if your iPhone isn't close by, you don't have to go running for it just to take or make a text or call. As long as you have an iPhone and are logged into the same Apple ID on all your devices, you can do both right from your iPad and iPad. It's not only easy to do, it's private and secure.
Keeping it relayed
SMS/MMS and calls are highly personal. If someone communicates with us, we want to make sure it's only with us. That's why Apple uses our Apple ID to make sure only the devices we're logged into are the ones that can send or receive our texts and calls.
For SMS/MMS relay, all devices have to not only be signed into our Apple ID in general, but signed in with iMessage in specific as well. For call relay, they have to be signed in with FaceTime in specific as well.
When you're logged into iMessage on all your devices, and your iPhone receives SMS/MMS, it will automatically forward them through Apple's messaging service and on to your iPad and/or Mac. It essentially turns SMS/MMS into iMessages, but still identifies them as SMS/MMS and colors them green so both the system and you know how they originated.
If you send a message from your iPad or Mac, it's sent up to Apple's messaging service, down to your iPhone, and then out over your carrier's network as a standard SMS/MMS.
As long as all your devices are all on the internet, even if they're on different networks, it will work. And it'll all be protected using the same end-to-end encryption as iMessage itself.
Calls for all
When you're logged into FaceTime on all your devices, your iPhone will send a message via the Apple Push Notification (APN) system to all your iPads and/or Macs at the same time. If any of them on the same Wi-Fi network as your iPhone, they'll present you with the incoming call interface.
Answer on your iPad or Mac, and your iPhone will transfer the call over using peer-to-peer technology similar to FaceTime audio.
Place a call on your iPad or Mac, and your iPhone will likewise be alerted over APN, and then relayed the voice data over peer-to-peer link.
In both directions, APN uses the same end-to-end encryption as iMessage, and the transfer uses a secure peer-to-peer link as FaceTime.
The bottom line
While SMS/MMS and call relay work differently — texts simply require all your devices to be online, calls require them to be on the same Wi-Fi network — they both ensure that only your iPads and Macs can access your messages and calls. They both also encrypt not only the notification of messages and calls, but the transmission as well.
That means all your communications are kept private and secure, which is just how you want them.