Are there technological benefits when presenting a "download page" that gives a message like the following?
Your download should automatically begin in a few seconds, but if not, click here.
Is there some bandwidth or server efficiencies with this? Or is it for the benefit of the user somehow? Why not just have your download link href's go straight to the url of the download?
Example page (one of a billion)
The benefit is not to the user, but to the site. They are forcing you to stare at their "download landing page" for a few seconds, while they show you ads. Furthermore, with that kind of chicanery, they can prevent the file in question from being directly indexed by search engines, while permitting the download landing page to be indexed.
The main reason why getting to a download takes as many steps as it does with most big download providers is indeed gaining page views, and producing ad impressions.
On the other hand, the "please wait" message has a real function IMO: The user is clearly shown that there should now follow a file download, and if redirection to the file download fails - for example because the link's broken, the server is overburdened or whatever - there is a way to try again, or to get help - important especially for less experienced users.
It also provides a soft landing (in the form of a splash screen, instructions, info...and advertising :) in the event that the browser does not react as anticipated.
For once you get additional advertising space. By delaying the download, you give the user some time to recognize and potentially click on the ads.
However a page like this can also be useful when you are offering lots of files. By presenting the user with a message stating exactly what they are going to download shortly, some might actually cancel their downloads by navigating back from that site. If the files you offer are big, this might actually save you some bandwidth.
Moreover you prevent the file from getting indexed directly in search engines, potentially bypassing your site completely. But you can let the search engines index your download pages with all the information about the downloads in them. This is related to the advertising topic, but also helps to keep your internal download structure hidden from the search engine. Should you decide to change it, there will be no broken links in search results.
Often you will also find a mirror selection on these interstitial pages. Users can conveniently use the time they have there to choose a different mirror than your suggested default. Should a link be broken, i. e. the mirror does not have the file (yet/anymore), by just hitting the Back button they can conveniently select a different one and try again.
If the site is telling you to wait a specific number of seconds before continuing, as you describe in the title, then it's likely all about advertising. But that's not the case with the Mozilla Firefox link you posted within your question. Here, I think the main point is to tell the user to be patient if the download doesn't start immediately, which it might not since it's an additional HTTP request that could be delayed for any number of reasons, including the download server being overloaded. That connection could be reset and the download might never happen. The message is trying to set appropriate expectations for the user: the download might not start this instant, but if it has been more than a few seconds and nothing has happened, then there was probably a problem and here's a link you can click.
There's also a lot of JavaScript in this page that tries to help with the download, and if that fails, the "click here" link should act as a failsafe.