What exactly is an embargo for a journal?
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...