There are several aspects, I would guess.
1. There is the view that you don't care. A great name is a great name, and a shitty name is .. .well, you know.
2. On the other hand, some people have a look at the WHOIS when dealing with a company/person in certain situations. So, it conveys that it's an old domain, and not something registered last week. For example, you find a website of a company you don't know, which is selling a product you may be interested in: It will change psychologically if the company appears to be in business since years and years (even if it's "fake" with an aged domain) whereas if it's very new, according to the whois.
3. Also, a LOT of people register constantly new names and search for new domains. You can kind of think that great names would have been registered a long time ago. There must be a correlation that most great names have been registered early, and didn't stay available to be registered now. This is very far from being 100% though (shitty names were also registered a long time ago and new great names are found). But this may have a small psychological aspect on buyers/sellers. You can argue it's (mostly) BS, but it may exist.
As for the price, it may be explained by the fact it's just a good name (and the correlation mentioned in 3. applies). When it comes to companies (where there are also "aged" companies sold, mostly for the reason number 2) or precious metals (where older stuff is more expensive, even without any real "collector" value), there are costs involved: Keeping the company in good standing for years (often it's companies which weren't used) or storing/insuring the precious metal has to be paid year after year. These costs are added to the sale price: The older, the more expensive. It's the same for old vine or cheese: Some costs pile up with time. and are including in the selling price.
Now, when it comes to domains, you could say the "age" doesn't bring much (it's not cheese or vine!). Well, there is the date appearing in the whois. And there is the fact that someone else would have maybe registered it if the person registering it earlier didn't do so. So, you fall on a "without the costs over the years, this wouldn't be available". Which is complicated (you could think you would be able to get it from someone having registered it later. It's not precious metal coins where there is a production at one time and it isn't produced anymore). There are many ways you can see it and many thought you can have on this. But anyway, I guess that's the "reasons" behind "age".
PS: It's mostly psychological, but as a buyer, if I try to sell you a 10K name and you look at the whois: If you see I registered it yesterday, you will know I didn't have to sit on it for years and pay renewal fees (assuming it was probably one domain among a lot of others), but I'm really only asking you 10K because I thought of the name (found it and registered it). It may appear less "justified" to you as a buyer. On the other hand, there's a name you want, you can have it for 10K, or you won't have it (that's what "first come, first served" is all about). What does it change if the guy is making 10K overnight or is barely just recouping his costs with all the domains he had to sit on for years? PSYCHOLOGY is often complicated (it may also work on the seller's side, about what is "justified" to ask or not. I would assume this is one of the reason why some put the age forward: "look how the price I'm asking for is justified. This domain is worth that price because it's old!").
