In essence, the kicker rail is a track that stops and and starts minecarts along a single strip of track. While it may seem similar to the powered rail, there are many important differences. It is crafted using a piston and a powered rail, and will drop both separately when mined.
How it works
If left in the "off" status, it will slow down and stop minecarts like a powered rail, but if it is left in the "on" status, it will neither stop or push minecarts, acting like a normal rail.
The magic happens when it is activated while a minecart is on top of it. When this happens, it will forcibly "kick" the minecart in the direction which it is placed, perhaps indicated by an arrow on the track's texture. This eliminates the need for a block at the end of a rail to change the direction of a minecart.
When powered rails are placed in front of the kicker rail, it will kick any minecarts within three blocks forward once activated. The kicker rail and powered rails cannot power eachother. When a minecart is in between two kicker rails, it will travel in the direction according to the closest kicker rail. In the unlikely event that a minecart is placed perfectly in between the two rails, it will travel in a random direction.
"Why should I ever use this?"
This rail allows you to make a simple station in which minecarts can be stopped and pushed from a single track without redirecting them into separate compartments. Other uses include controlling traffic and creating traps in which minecarts can be forcibly pushed into danger at the passenger's surprise.