Once an avocado is cut, it gets brown pretty quickly. It's still edible, but not that attractive. If you want to keep the saved avocado half or a bowl of guacamole green, store it with a red onion.
The video above from CHOW shows a red onion can preserve the avocado for longer than other common approaches (lemon juice, plastic wrap and tap water). Cut up a red onion and put it at the bottom of the storage container. Store the avocado on top, with the skin side down. (Because the skin is touching the avocado, you don't get the onion flavour leaking onto your fruit. The red onion also is milder than yellow onions.)
You can also store big chunks of red onion on top of guacamole to keep it fresh and presentable for longer, as the video at right from About.com shows. This video, though longer, demonstrates a number of other techniques commonly used to preserve avocados — but the red onion still wins, followed by using lemon juice. (You could also use lemon slices for this trick.)