Well, it does say in its conclusion: "The basic thesis of this article is that organizations which design systems (in the broad sense used here) are constrained to produce designs which are copies of the communication structures of these organizations." [0]
I actually cited Conway's law to convince a senior decision maker that his organisation was badly structured. Briefly, a civil service organisation acquired systems for various users in a large customer organisation. The systems were rarely technically compatible although were often doing very similar things. This complicated technical interoperability and increased through life costs (e.g. because they had separate support contracts that duplicated basic functions).
The incompatibilities often resulted because the systems had separately written user requirements (e.g. using different terms for the same things, describing common processes in different ways). The requirements were incompatible because they were written by independent acquisition teams. The acquisition teams were independent because they reported to and were 'owned' by different parts of the overall customer organisation. Recognising this fact allowed the senior guy to request that the various customer teams established consistent terminology, processes and support contracts. In other words, going for coherence by design rather than (expensively) retrofitting it.
[0] https://web.archive.org/web/20190919111512/http://melconway....