An integrated (or knit-in) waistband means the waistband is knit as one continuous piece with the rest of the garment—there's no separate elastic band stitched in. This creates the lowest-profile waistband you can get, which is great news under tight ski pants or layered outfits. You won't feel any digging, rolling, or visible lines.
The comfort factor is a real standout. Without a separate band, there's nothing to pinch or shift around during a full day of riding. It's especially nice on long lift rides when you're sitting against a hard surface and every seam counts.
The one tradeoff: because the stretch is built into the knit rather than reinforced with elastic, these waistbands can lose some elasticity over time—especially with frequent washing. If you want that barely-there feel under your layers and don't mind replacing your base layers every few seasons, knit-in waistbands are a premium choice worth considering.