What exactly is an embargo for a journal? I was trying to access this article and was told this journal is "embargoed" for more than a year. This is the first time I have seen the term embargo used in an academic setting.

This answer talks a bit about the idea of journal embargoes. Wikipedia has more information but I do not find it helpful at all.

As I read (on Wikipedia), it seems embargoes in journals are for future stories (and not for everything ever published). The article that I am seeking is from two years ago.

This question implies that embargoes deal with the relationship between publisher and author, which does not make sense in the context of my request.

This answer implies that embargoes are about limiting access electronically, but, again, it seems I can buy the article for $40 so clearly it is available electronically.

So, what exactly is an embargo (in this context)? Does it really mean that I simply have no access to this through my university account? It looks like it is available to the general public (if you pay) but not to those of us with access through university subscriptions.
So far as I know, your understanding of the typical use of "embargo" for journals is correct: it is when a journal wants to be the "first to press" with its article, and so places a gag order on the authors and their institutions so that they don't go talking to the press first.

There is another place where journals also often want to be "first to press," however, and I suspect that this is what "embargo" refers to in this case. It is often the case that a journal makes its content available through multiple routes: immediately through the publisher for a premium, and with time-lag through larger accumulations, such as PubMed or ScienceDirect.  

Thus, I think that what is probably going on here is that your institution does not judge this journal important enough to subscribe to directly, but gets it as part of a time-lagged "package deal."  You should check with your librarian how long the time-lag is, and then decide whether it's worth waiting or if you want to ask a colleague to help you get around the paywall...