Just a small tweak to that explanation. Rather than the year of manufacture, it's the year of the design. It could have been manufactured that year or sometime thereafter. Some models had multiple design iterations, while others were manufactured for many years using the same design.
Are you sure? I've always heard that the first two digits are the year it was made, in years since 1960. Never heard of it denoting design iterations.
That was my initial understanding too, but further digging into them a while back clarified things a bit. Beginning in 1960, they started using a three digit prefix (which became four digits in 1970), followed by a letter indicating country of origin (A for the US, J for Japan, G for Germany, etc.), then a sequential serial number.
The prefix identifies the release date of the major engineering revision that the instrument is built to - the first one (or two, for the four digit prefixes after 1970) digits added to 1960 will give the year, and the last two are the week. Eg. 710 would be the tenth week of 1967; 2245 would be the 45th week of 1982. To more accurately date the 'birthday' of the unit, you'd need to go inside and find parts with date codes. While they wouldn't tell you with 100% accuracy how new it was, you could be sure it was not older than its newest part (this of course is based on the part in question being original to the instrument).
Some instruments were revised fairly quickly and the engineering rev dates track their production closely; others stayed the same for a long time. For instance, I have an Agilent labeled 8644B signal generator that has a 3546 prefix - late 1995 engineering revision. The component dates indicate that it was made in late 2000 at the earliest.
-Pat