Where skeuomorphism said "look like the real thing," flat design says the opposite: the screen is a screen, not a pretend sheet of paper or leather. Icons become flat silhouettes or uniform-weight lines; buttons are told apart by color contrast alone, no shadow.
There were practical reasons too. As high-density (Retina) screens spread, shipping elaborate gradients and texture images at multiple resolutions got expensive, and simple vector shapes were just easier to handle responsively.
Push flatness too far, though, and people can't tell what's a clickable button versus plain text — the "flat design discoverability problem." The industry later settled on "flat 2.0," adding back a touch of shadow or contrast for that reason.