From the Food Lab

From the web site, Serious Eats

http://www.seriouseats.com/2012/01/the-food-lab-the-best-guacamole-avocados-science-browning-ripening.html#continued 

On Browning

Of course, we've all seen those avocados that seem perfect on the outside, but once you cut into them, a series of deep brown stripes and striations appear. What's up with that? Unfortunately, it's not something that can be predicted or prevented. It's caused by uneven enzymatic action inside the avocado as its developing and is exacerbated by extreme weather conditions as the fruit develops.For Hass avocados, you can expect the likelihood of this phenomenon to increase starting in December and maxing out around February (ack, Superbowl season!).

What about leftover avocado? Any way to keep it from browning? Oxygen is the enemy of avocados—it's what causes them to turn that unsightly brown. Plastic wrap works alright, but even plastic wrap is oxygen-permeable. My avocados didn't last more than about 8 hours wrapped in plastic before visible browning occurred.

The old rub-with-oil-and-place-face-down-on-an-oiled-plate works fine if you've got a perfect half of an avocado with a smooth face, but it doesn't help if you've got, say, 3/4 or 1/4 of an avocado.
The better solution in that situation? Just submerge the sucker in water. I store my unused avocado pieces in a plastic container filled with water in the fridge for up to overnight. Perfect, oxygen-free seal for any shape, and because an avocado is so dense and high in fat, water is slow to penetrate it (it'll eventually become softer).