Why does a light object appear lighter in your peripheral vision when it's dark?
Short answer
Peripheral vision is more light-sensitive than central vision.

Background
When you look directly at an object the image is projected onto the fovea. The fovea has maximal visual acuity (high resolution) and a high density of cones, which are specialized photoreceptors to sense colors. However, cones are not very sensitive to light.

Here is a picture showing the foveal field of view:


Source: Pinhole Eyeglasses

If you look at the same object using peripheral vision, the image is formed more eccentrically on the retina. Here, cones are sparse, but high densities of rods are present. Rods do not detect color, but are much more sensitive to light than cones. In fact, they can faithfully detect a single photon! (Webvision) Moreover, many rods converge onto a single ganglion cell, and rod responses are therefore summated. This spatial  summation further increases light sensitivity in the periphery, but degrades spatial resolution.

Here is an image on rod and cone distributions on the retina, showing a high cone-density in the fovea and a high rod density more eccentrically:


Source: Webvision

And here is an image showing the higher light sensitivity of rods over cones:


Source: Webvision

Hence, peripheral vision is more light sensitive because: (1) there are more rods in the peripheral retina; (2) rods are more light sensitive; and (3) eccentric retinal rod circuitry further amplifies the rod responses. However, color perception and spatial resolution are better developed in the central field of view.



Further reading (Cognitive Sciences.SE) 


Rod and cone distributions: "Why can we not see around our point of focus of our eyes?"  
Visual acuity as a function of retinal eccentricity: "Visual acuity and offset stimuli"