How can I make the introduction of a paper more "scientific" and less "popular"? I am a master's student about to start writing my thesis. After I wrote my research proposal, my advisor said that when I write my thesis, I should make it less "popular" (I believe he referred mainly to the introduction, where I presented the field and the subject in a rather detailed manner and broke it down in a way that average people could understand why I am proposing to do this research) and more "dry" and "scientific". 

So I'm assuming he means that I should strive to direct the text to experts (as scientific publications usually are), and not begin from the very beginning of the subject and not "build up" the introduction too slowly.

The problem is that I always feel that I DO need to explain the background when starting to write a new piece, as each text stands on its own and should be complete in itself. I need to find some way to set the stage on one hand, but not too tediously on the other hand. I guess this is part of the art of writing, which develops through experience, but I was hoping someone here could offer some helpful ideas to achieve this.

I found this question and its answers related to my question and interesting to read, but that doesn't answer my question.
This is a common issue when inexperienced people write their first papers. It's tempting to write down everything that went into your personal understanding of a subject, rather than just starting from what's known and focusing on the new things you did.

Imagine if you looked up a recipe for a pie and the first 80% of it detailed the history of wheat cultivation, how wheat is made into flour, the way the tablespoon and teaspoon were defined as units of measure, statistics on the average consumption and enjoyment of pie throughout the 20th century, and so on. Imagine if you looked up the text of a new regulation and it started with "This law could be passed in our state legislature because, in 1773, the Boston tea party...". Imagine if a car repair manual started with the history of the wheel.

It's important to tell the public why science is important and why your studies make sense, but a paper isn't the place to do it. It's also not the place to give a full exposition of every technique you used. If you must, just put references to review articles or textbooks.