The white side is the "standard" reflector, and it casts a soft light back onto your subject. This is perfect for if you are shooting outdoors and in situations with lots of light as the light reflected is reasonably soft and muted. In very low light you won't get much of a reflection off this one (or you will have to put it quite close to your subject) so you are better with the silver in that situation.
The silver side reflects a stronger light back onto the subject, so is better suited to lower light situations, or where you want a very strong light - it's too harsh to be used on a sunny day for example as your subject would't be able to look at it! The color it reflects back is fairly neutral. Handy to have for use indoors with low light.
Again, this casts a slightly stronger light, but also gives a warmer hue to the subject. This isn't something I use a lot as I prefer to warm things up in processing if need be, but I have heard that it is good in backlit situations when the sun is quite low in the sky.
This isn't actually a reflector but in fact the opposite - this absorbs light instead of reflecting it back. You would use this if you wanted to create a shadow - perhaps if you had light coming in both sides and you wanted to create depth in your portraits by blocking light to one side.
If you take off the reversible cover, you will see that the middle is a translucent disc, called a scrim or diffuser. You hold this above your subject to diffuse the natural light and make it softer - great in sunlight to tone down that harsh light - or you could even put it in front of a window if you wanted to diffuse some of the light coming in.
If you don't want to fork out for a reflector, a large piece of white card will work the same as the white one, or cover it with tinfoil to create a silver reflector (or gold foil for the warmer hue) DIY reflector in minutes!