Snap closure cuffs use button-style snaps to set the cuff tightness at a few fixed positions, rather than the infinite adjustability you get with velcro. You'll mostly find them on casual or retro-styled jackets rather than technical riding gear.
The downside is that snaps offer limited adjustability, so you can't fine-tune the fit around different glove styles or wrist sizes. More importantly, snaps can freeze up in wet, cold conditions, making them frustrating—or even impossible—to open and close with gloves on. Velcro doesn't have this problem.
If you're doing any serious resort riding or backcountry work, snap cuffs aren't ideal. They're fine for mellow lodge-to-lodge days or if you're drawn to a vintage look, but for keeping snow and wind out on a real mountain day, velcro cuffs (especially with an inner gaiter) are a much better bet.