A vertical fly is the traditional front opening you'll find on most men's base layer bottoms—it works just like the fly on your regular pants, with an overlapping fabric closure running top to bottom. It's the most common style out there, so if you've worn men's thermal underwear before, you're probably already familiar with it.
The main advantage is convenience and familiarity. It's intuitive to use and doesn't require any adjustment period. The trade-off is that the overlapping fabric creates a small amount of bulk at the front, which you might notice under tight mid-layers or a fitted ski pant.
For most resort skiers and riders, a vertical fly works perfectly fine. If you're layering loosely or wearing standard-fit snow pants, that slight extra bulk won't be an issue. It's really only worth considering an alternative like a horizontal fly if you're going for an ultra-slim layering setup where every millimeter of bulk matters.