What does 1:4.5-5.6 mean?

This ratio tells you the maximum aperture available on the lens. The aperture is expressed as a ratio, so 1:4 is f/4, 1:5.6 is f/5.6 and so on. Many zoom lenses have a variable aperture, which changes as the lens is zoomed. Take this Canon EF 100-400mm f/4.5-5.6l IS II USM – at 100mm, the maximum aperture is f/4.5, but it gets smaller as the lens is zoomed in, down to f/5.6 at 400mm.