Both in the wild and in captivity, budgies like a little privacy when they're nesting. For a pet budgie, this typically means taking shelter in a nesting box. Even if you don't plan on intentionally breeding budgies, giving them a nesting box can prevent impromptu nests from forming in less convenient places when they spend time outside the cage, so give your birds a place to hide out should they so desire.
Nesting Box Exterior
The nesting box is a particularly plain-looking wooden box that you attach to your budgies' cage. A small opening in the cage allows your budgies to come and go in and out of the box, which has a small entry point just large enough for your birds to shimmy through. While it may seem rudimentary on the outside, the box does not need to be specially adorned to entice your birds -- they'll either choose to go in or not, but either way, they know what to do with it.
Inside the Box
The inside of the nesting box is slightly more decorated than the outside. Typically, a nesting box has a concave block inside -- your birds use this as the actual nest, and lay the eggs in it. To help protect the eggs, you may line the concave block with white pine shavings from the pet supply store. This emulates the lining that a budgie would collect in the wild.
Nesting boxes are designed to imitate the type of nesting environment budgies find appealing in the wild. In their native Australia, female budgies seek out and determine where they will nest. These nesting spots are typically in natural cavities, either in trees, logs or man-made objects like wooden fences. Wild budgies collect soft material to line the nest, and in which to lay their eggs -- much like the white pine shavings you use in a nesting box.
Without the Box
The nesting box serves an important purpose for your budgies, because while they prefer to use one, if they don't have that option, they'll find an alternative. For example, you may notice your budgie ripping up the paper at the bottom of her cage in an effort to form an impromptu, soft nesting site. If left unattended outside of the cage, she may lay her eggs in any inconspicuous place she can find, like behind or on furniture.