I bought a cast iron grill pan from a famous Swedish four letter store. And they suggest to boil milk with some vegetal oil before starting to use the grill.
Why is this necessary, and what difference between just washing with water?
I've never heard of milk being used to season a pan and so I am a little skeptical of it.
Pan seasoning is always done with fat that is heated until it polymerizes. This creates a very hard non-stick surface that makes cooking easier and protects the pan from rust.
See this question for more about how to season your pan:
See the article linked in one of the answers:
This process, while slightly more labor intensive, produces the best seasonings I've ever seen.
i had to do this when i bought a non-stick pan from the same place, and it didn't make an ounce of difference. if it's truly a cast-iron pan, there are much better places to get info on proper seasoning, like the links posted by Sobachatina, above. if it's a non-stick type coating, like the one i bought, just keep using it. it's gotten much better over time.
The milk-and-oil process isn't there to wash the pan, it's there to 'season' it. The seasoning process embeds oil in the pores of the metal, which increases its resistance to water - the last thing you want is a rusty pan (though a nice layer of black oxidation is a good thing).
You should avoid washing a cast iron pan with soap and water as it will remove the seasoning. Just give it a good wipe or go over it with a brush.