Here's one I do understand: Suppose you want to exfiltrate some data out of a network without raising alarms. One way to do it is to set up a DNS server. Basically, you use DNS itself as a communication method, not merely a lookup table.
I've never actually used it, but it always seemed a cool idea. Almost no one blocks DNS, which means you can send data from anywhere in the world in a very unexpected way. You'd of course want to keep the transmission size reasonable (perhaps 5GB of DNS traffic might raise some eyebrows) but any system that you can `nslookup foo.com 8.8.8.8` on, you'd be able to `nslookup foo.com <your special server>` on. So this technique works in almost every case, except extremely monitored systems that only allow outgoing connections to a specific set of restricted IP addresses.
But for the special network protocol that the NSA uses to access backdoored NICs, I forget why it works, since the packet would need to pass through many routers along the way. In fact, I feel like I'm misremembering. Most target computers are behind routers, so it really doesn't make sense. Maybe it's a technique used against routers themselves. All I remember is that the NSA has some type of "signals we can send which normal networking tooling doesn't detect at all," along with a dose of "we know Iran just ordered some new servers, so we intercepted the servers and installed a backdoor." (The latter is called TAO: https://en.wikipedia.org/wiki/Tailored_Access_Operations)
They definitely do something with NICs though. The ANT document (https://en.wikipedia.org/wiki/NSA_ANT_catalog#Capabilities_l...) shows "COTTONMOUTH-III is a stacked Ethernet and USB plug costing approximately $1.25M for 50 units." Must be one hell of a plug.
https://en.wikipedia.org/wiki/NSA_ANT_catalog#/media/File:NS... is also pretty neat. It's a USB airgap bridge, i.e. janitor walks up and plugs it in to the target device. I wonder what the range on stuff like that is... Seems like you'd have to be sitting outside in a van or something, which is rather hard to do if your target is a nuclear enrichment facility (stuxnet).