I've googled hallows and this is what it came up with:
Definitions of hallows on the Web:
name used by some traditions for Samhain, or Halloween
[url]crypt.eldritchs.com/wicca/glossary.html[/url]
("holy" or "holy night") the Oct. 31 Greater Sabbat, also called November Eve, the Celtic Samhain ("sow-en"); the beginning of the Celtic winter, and of the Celtic year; the beginning of the Witches' Year, when the Veil Between the Worlds grows thin and the spirits of the dead may return to Earth; the Descent of the Goddess to the Underworld; the final Harvest festival
http://www.ravenquest.net/WyldeWoods/h.html
I like the bit about the Veil between worlds grows thin and spirits of the dead may return to earth. It could indicate more interaction with the veil in the ministry. We definitely need more information on it as it was very vague about what it was and why Lupin knew that Sirius could not come back through it. i don't know how it could be involved - i doubt the ministry would just let harry come in and have a look around whenever he fancied it. not when he refused to be the poster boy for scrimgeour. maybe he'll take a low level job there that would allow him better access, rather than going back to hogwarts.
it could mean the less interesting breakdown of the barrier between magical and muggle worlds - there was certainly more magic in the muggle world in HBP. But i hope it the veil in the MOM - that has far more potential for your imagination i think.