What do these numbers mean at front of my two cameras?

Samsung camera: 3.9 - 58.5mm 1:3.2-5.8

Nikon camera: 4.5 - 81.0mm 1:3.5 - 5.9

Added (1). Does it mean that the samsung camera has wider angle and lets more light in in dark situation (for existing light photography)?

Added (2). Does it mean that the samsung camera has wider angle and lets more light in in dark situation (for existing light photography)?

You are correct.

The 3.9-58.5mm/4.5 - 81.0mm is the focal range of the lens and the camera specifications should give you a full frame equivalent (like "35 mm equivalent: 18-270 mm").

The 1:3.2-5.8 is the maximum aperture. At the wide end (3.9mm), the maximum aperture is f/3.2 and at the zoomed in end (58.5mm), the maximum aperture is f/5.8.