Standby power refers to the electrical power an appliance draws just by being plugged into the outlet. This is also referred to as "vampire" or "phantom" load because the appliance is just sucking power from your wall (and money from your wallet).
Just about all appliances use standby power to keep them ready to turn on when needed. Any device that displays a time (microwave, cable box, coffee maker) or has any light on it (battery charger, flat screen tv, etc.) is using standby power. Your cell phone charger that stays plugged into the wall all the time also uses standy power when not in use.
The only way to prevent these devices from consuming this power is to unplug them from the wall or use a surge protector (a.k.a. power strip), and turn it off when not in use.
Lawrence Berkeley National Laboratory has one of the best sites dedicated to standby power. From the home page:
...a typical American home has forty products constantly drawing power. Together these amount to almost 10% of residential electricity use.
The site has a great chart showing how much standby power is consumed by appliances. In other words, how big their vampire load is.
By using the The Energy Detective (TED) I was able to see how big my total home's vampire load was. To do this, all I had to do was turn off my heating and AC, any lights and office equipment that was on, and make sure any TV's were off.
Anything else that was plugged into the wall was switched to "off" but still drawing a tiny bit of power. With everything off in the house, the house's vampire load was around 200 Watts. If I leave for a vacation and turn everything off but leave the standby loads plugged in, my home would consume 4.8 kWh in one day (200 Watts * 24 hrs)! While this only comes out to about $0.48 a day (I pay around 10 cents/kWh), that is still almost $15 bucks a month just in wasted energy I'm paying for.
The strategy to combat vampire load power loss is to simply unplug things when not in use! That means everything you can stand to have unplugged (but be careful you don't miss any shows by unplugging your DVR!). Only plug things in when you need them and you'll see some nice savings!