A Digital Notary client application would submit a hash value (which in the early days was a combination of MD5 and SHA-1 but the system was very flexible in that it could upgrade the hash algos when more collision resistant versions became available) that would become part of a Merkle tree along with any other client submissions received in a short timeframe. The parent "top hash" node of the Merkle tree was then hashed with the the last value in a linked list referred to internally as the "super hash" chain to create a new end value in the chain.
The client application would receive a notary "certificate" containing all the values in the Merkle tree required to re-calculate the hash woven into the super hash chain along with the timestamp for the moment it became part of the chain. The client application could use this certificate at any time to electronically verify the veracity of any "document" (i.e., guarantee that the document existed in its exact form at a specific point in time.)
On a side note, the algorithms and implementation were successfully tested in court cases. (Some of Surety's customers used the system to timestamp millions of documents turned over in electronic legal discovery to ensure they were not tampered with by opposing counsel.)
The New York Times value was only significant in that if could be used to "manually" calculate the veracity of the notary certificate by hashing the super hash value it contained with all subsequent values in the super hash chain until it resulted in the hash value published in the Times. This "widely witnessed" approach made it impossible for an insider to collude with someone to generate a correct notary certificate retroactively by replacing the document with a forgery.
The blockchain technology used by crypto currencies is similar except for the tremendous amount of computation required to generate a "correct" hash value to close out a block and weave it into the chain.
Stuart Haber and Scott Stornetta deserve a lot of credit for creating this when were working for Bellcore. Two brilliant guys.