When you replace brake fluid you are "flushing" the system. The way you do it, all old break fluid will be removed and new fluid in its place.
You should do this as your owner's manual prescribes. I believe normal intervals are either two or three years as your manual says. Some manufacturers may have something else, so start there first. The reason for this is that brake fluid absorbs water over time. When fresh fluid is in the system, the fluid is in a dry state. When it gets old and absorbs water, it is in a "wet" state. Depending on the fluid you are using (usually DOT3 or DOT4), as brake fluid becomes wet, it will boil at a lower temperature. This becomes important, because as you use the brakes, the fluid gains temperature due to friction of the brakes and such. As the fluid gets older, it has the propensity to boil easier, which will cause bubbles in your brake lines. These bubbles will compress where the liquid will not, thus reducing the effectiveness of your braking system.
To change the brake fluid, you start by bleeding the brakes at the furthest point away from the master cylinder. In left hand drive cars (US), start at the bake right. For you peoples across the pond, I suspect your master cylinder is on the right side of the car, so start with the back left. Then go to the opposite side and do the other rear brake. Then move to the front on the side you started with. On four wheel vehicles you only have on wheel left. When you are done with all four wheels using this method, all old brake fluid will have been changed. This can be accomplished using a power bleeder, or the old have a friend pump the brakes for you.
In my opinion, the brake fluid is one of the most overlooked maintenance items in your vehicle. People just don't think about it unless there is a leak.
EDIT (to answer your edit):
It seems the general rule of thumb for replacement is recommended at two years. You can tell how your own brake fluid is doing by shining a flashlight through the liquid (easy on a white plastic type master cylinder ... take the top off on older metal reservoirs and shine the flashlight down into the liquid). When brake fluid is new, it has a very light amber color to it. As it gets to the point of needing changed, it becomes a darker amber color. It may even get to the point where it is dark brown or even black.
As for the price you were quoted, my first rule of thumb is ... stay away from dealerships for regular maintenance items (like oil changes, radiator flushes, brake fluid replacement, etc) unless you get free scheduled maintenance from them. This is just my opinion, but my experience tells me dealerships overcharge on these types items. Chain stores are not going to be much better as far as cost and they tend to try and do add-on items (ie: you go in for an oil change and they tell you you need to have x, y, and z done as well). Find a smaller local maintenance shop you can trust (usually found through word of mouth) and use them. Your cost is going to usually be the best at these locations. Mind you, there are always going to be deals to be had, keep on the look out for these from your dealerships. Other than cost, there is usually no problems using a dealership, so please do not misunderstand. In the US, there is no requirement to have maintenance items accomplished at a dealership to maintain your warranty. (I'm not sure about the legality of this in other countries.)
About the dealership, you said "they were going to hook it up to a sort of dialysis machine to "flush" it out." This cracks me up because this is normal operating procedure for a single mechanic (without help) to perform this service. It actually makes it easier, quicker, and cheaper (less man hours) for them and they want to charge more for it. It appears by quite a bit, actually. I cannot tell you what the price would be, but shop around a little bit and you are probably going to find a better price.