Zeer is a bit more formal and a bit old-fashioned. It is still used, but not as common as heel.
I know that zeer means very. But I tried to answer "It is quite important". Does anyone know why is this answer wrong?
Quite is not strong enough, I would translate quite important to Dutch as redelijk belangrijk or best belangrijk.
Sounds too strong to me, maybe there is some context in which that is the case, but not this one. I would translate extremely important to extreem belangrijk. And there are zeer, heel and erg, which are closer to very, so I don't see the need to go extreme here. ;)
But.... it does not seem to me as if there is any context given at all in the question, so I don't see why it could not be 'extremely important', which is maybe slightly stronger than 'very important', but not as strong as 'vitally/crucially/critically important'. In my opinion, without context, any of these options would be a fair translation.
Can someone explain to me the difference between "zeer", "veel" and "heel" as in "very"? I am not sure when to use each of them.
See above :) I agree with user Confessing: zeer and heel are pretty much interchangeable, but zeer is less common and slightly more formal.
The Dutch word veel is a determiner, and means much/many. As such, it might seem similar to heel/zeer (=very), but these are adjectives, and are therefore used differently. I hope that's clear enough for you :-)