'Varje' can be translated as 'every' or 'each' - most of the time both work, although there is a slight difference in meaning ('each' puts the emphasis on the individual item, which 'every' focuses on all of the items/the totality). There are also some situations where you have to use one or the other. (Here is a link that might be helpful:(http://www.bbc.co.uk/worldservice/learningenglish/youmeus/learnit/learnitv110.shtml)).
For me, "every day" where it refers to a repeated event is one of those situations where it would feel strange to use 'each' but as it sometimes seems to be used by native speakers in this way, 'each day' is now accepted as an option. However, it might be better to use 'every day' as 'each day' may sound unnatural to some native speakers.