Jensen's alpha, as you may recall, is a risk-adjusted measure, that can be viewed as excess return that takes beta into consideration. The typical way we view excess return is:
Jensen's alpha looks a bit like this expression, but with a twist:
First, we're dealing with equity risk premiums (portfolio return minus the risk free rate). But, basic knowledge of algebra would make it clear that if this was the only difference, it would match our excess return. What's really different is the use of beta. Jensen's alpha takes the portfolio's beta and applies it to the benchmark (or more precisely, the benchmark's equity risk premium), essentially saying that THIS is what the portfolio's return WOULD be (net the risk free rate), if beta captured everything for the portfolio; that is, if beta was a perfect predictor of portfolio return. But, Jensen's alpha is usually not zero, based on the portfolio's idiosyncrasies.
The military doesn't permit much in the way of variation. But, when I was on active duty (with the Field Artillery branch of the U.S. Army) we had the option of substituting "airborne boots" for our standard issue ones; they looked much sharper, and many of us did (even if we weren't airborne!). And, one could buy their "dress blues" off the rack, or get them custom made. And so, even here we had the ability for some degree of idiosyncratic adjustments.
This difference is like what we see with the result from Jensen's alpha. When one speaks of "portable alpha," THIS is the "alpha" they are speaking of: the part of excess return that is completely attributable to the idiosyncrasies of the portfolio, with no baggage from the benchmark.
By the way, you are probably also noticing that we use the term "alpha" here, but in the "Jensen's alpha" context. Whenever anyone simply says "alpha," you should ask "what alpha are you referring to?" This isn't an offensive question, but rather an insightful one, because it reflects your awareness that there are at least two versions of alpha: basic alpha, which is derived from excess return, and Jensen's alpha.