What is it? In a sense, it is straightforward: the a priori, the epitome of something absolute and unchanging, is historicised and thereby becoming a historical a priori, having a particular place in history, ie. it is seen as a part of historical development, changing through history. What exactly is meant depends on the author. Dilthey, Husserl, and Foucault may roughly have meant the same - that the a priori of each person (that which structurally pre-forms their knowledge and cannot be changed by them) is dependant on their relation to their Lebenswelt and that these person - Lebenswelt relations undergo change through history. For example, the formative structures of (the possibility for) knowledge were quite different for monks in 13th century monasteries from free authors or professors in the secular Berlin of the 1920s.
Generally, it is a concept emerging from Hermeneutics and most prominent in this context. If you think about the absolute limits of understanding (both oneself and a text), you naturally reach the conclusion that you have to do so from a particular social, cultural, and historical situation that forms your language, how you think, and what you even are able to think. The historical a priori is merely an emphasis of that which is roughly the same yet still changes through history: reason and reasoning about the conditions of (the possibility of) knowledge. In my answer you linked I dropped the mentioning of Husserl exactly because of that: In his phenomenology, this is treated a bit as an afterthought instead of as the preliminary lines that have to be drawn.
For Husserl and Foucault, this issue does give a good overview of the systematic place, need for and problems with their particular conceptions. For Dilthey, there is a rather recent book in English that can shed some light on his project. Generally, Georg Misch's reconstruction of Dilthey's thought is the best I have encountered so far but I dont even know whether there are translations from German available.