I'm sure that there's a very scientific explanation behind it, but it all comes down to the fact that opposites attract and balance each other out - a statement that is true in all aspects of life. When it comes to beauty we see this when red and rosy skin is neutralised with a green corrector or primer, and blonde hair is kept bright (not yellow) with the help of purple.
I've tried different shampoos and you can find one form or another of them in almost every shop, but at the moment I use the John Frieda Sheer Blonde Colour Renew Shampoo & Conditioner. For me they work really well. I get a nice, clean and crisp brightness from the shampoo while the conditioner helps to keep my hair soft. I do find that the shampoo can dry my hair out - particularly if I don't follow up with the conditioner or even better a rich nourishing treatment. I'm not keen on the smell of either of the products though. I find them quite perfumed in a strange artificial way, but fortunately that doesn't last long on your hair.
The current packaging looks slightly different than in the pic, but it is the same as the product above
They are a great and affordable way to keep the colour you want between salon visits, removing nasty brassiness and after all - what's the point in spending lots of money in the salon and then not maintain your hair properly?
If you are new to these tone correcting shampoos - don't have a panic attack the first time you try one. They do have a very strong purple colour, and you MUST MUST MUST follow the recommended time on the packaging - otherwise you might get a colour that Dame Edna would envy.