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Nagle's document, Congestion Control in IP/TCP Internetworks (RFC896) describes what he called the 'small packet problem', where an application repeatedly emits data in small chunks, frequently only 1 byte in size. Since TCP packets have a 40 byte header (20 bytes for TCP, 20 bytes for IPv4), this results in a 41 byte packet for 1 byte of useful information, a huge overhead. This situation often occurs in Telnetsessions, where most keypresses generate a single byte of data which is transmitted immediately. Worse, over slow links, many such packets can be in transit at the same time, potentially leading to congestion collapse.
Nagle's algorithm works by coalescing a number of small outgoing messages, and sending them all at once. Specifically, as long as there is a sent packet for which the sender has received no acknowledgment, the sender should keep buffering its output until it has a full packet's worth of output, so that output can be sent all at once.