How did the early internet nearly choke itself to death, and what stopped it?

It slowed to a crawl because computers were trying too hard to help. In October 1986 the backbone of the early internet dropped from its capacity of 32 thousand bits per second to 40 bits per second, a drop of three orders of magnitude. That state is called congestive collapse: the network is busy, but almost nothing useful gets through.

The trap is easy to fall into. When routers receive more packets than they can handle, they discard many of them and expect the endpoints to resend. But early TCP resent badly: when packets were lost, the endpoints sent extra packets repeating the lost information, doubling the incoming rate. Aggressive retransmission can keep a network jammed even after the original load has dropped, so the same network can sit in two stable states under the same load, one healthy and one collapsed.

The fix was to teach every computer a bit of manners. The correct behaviour is to repeat dropped information, but progressively slow the repetition rate. If every endpoint does this, the congestion lifts and the network resumes normal behaviour. Van Jacobson and Sally Floyd's congestion control did this. It was implemented in end nodes between 1987 and 1988, and in 1988 Jacobson's solution reached the BSD UNIX as open source. Congestion lifts when every endpoint backs off together.