On an SLR/DSLR with an optical viewfinder, the camera keeps the lens wide open so the viewfinder stays as bright as possible. That makes composing and focusing easier, and it also helps autofocus systems, which need plenty of light.

The depth-of-field preview button temporarily stops the lens down to the chosen aperture so you can see the actual depth of field before taking the shot. The tradeoff is that the viewfinder becomes much dimmer—especially at small apertures like f/16 or f/22—which is why cameras do not show that all the time by default.

Live view is different: it is an electronic image from the sensor, so the camera can brighten the display electronically, raise gain/ISO, or simulate flash exposure. That can make the screen look usable even when the optical viewfinder would be very dark. But that electronic brightening does not change the fact that an optical viewfinder can only show the real light coming through the lens.

So the DOF preview button exists to let you check depth of field when you want it, without making normal viewing and focusing unnecessarily dark all the time.