If I remember correctly, in the book Skunkworks they explain that it would increase the air pressure. The analogy made was that it was similar to putting a finger on a garden hose to partially block it, thus increasing the water pressure.
Obviously there must be some complex physics going on but that was the gist of it.
Probably someone with more knowledge can confirm or correct me :)
Since the SR-71 is a perennial HN favorite:
https://news.ycombinator.com/item?id=13567554
I think the StackExchange answer linked below covers interesting aspects of supersonic inlet behavior, but doesn't do a great job answering your specific question.
Here's a great answer on avation.stackexchange.com that answers that exact question:
I've often heard this (also about the bypass in Concorde's engines), but I've never heard a clear explanation about how some element of an engine which doesn't involve burning fuel can generate thrust. Can anyone explain it?