This simple Military Policy lets you build the most militaristic District and its buildings more efficiently. However, depending on how many Military Policy slots you have available in your government, it may not be worth your while - a 30% boost isn't such a big deal, and unless you're constructing Encampments and/or buildings in them in multiple cities, then there are other Policy cards which are more useful (such as Conscription). But if you have more than 1 slot, and no pressing concerns, Veterancy will speed up these constructions.
Of course, don't forget to use it only when you are actually building the aforementioned district and buildings, and then swap it out.
In Gathering Storm, Veterancy also accelerates the construction of the Harbor district and its buildings. Given the Lighthouse's value of providing Food, Housing, and a Trade Route, Veterancy can now give a boost to your growth, not just your military.
The term “veteran” comes from the Latin vetus, meaning “old” (just don’t refer to one that way). Although there had been those lucky ones who had survived military service before, it was the Romans who established the practice of honoring survivors with privileges and rewards. Any non-Roman soldier honorably discharged was granted Roman citizenship (not to be taken lightly). The normal term of enlistment was 25 years, and upon discharge, both Roman and non-Roman veterans were given pensions (the praemia, established by Emperor Augustus) and land grants, usually on the frontiers. Since Roman veterans were subject to recall, the latter meant that reinforcements were never far away when barbarians invaded.