Is the order of authors' names important? I am trying to publish a paper based on my MSc. thesis in software engineering.
I have considered myself, as the first name of the paper, and my supervisor as the second one, since I was the person behind everything. He was much concern about the structure of the thesis, and in scientific contribution, his share was something around %16.

But someone told me, a supervisor should always be the first name, because he has supervised the research. Is it true? But, i think it is not fair?

The questions are:

1- Does the order of authors' names convey some message?

2- Is it true that supervisor should be the first name?
The answer depends on the field of research. For example, in most areas of mathematics and some of theoretical physics, authors are listed alphabetically. In other fields this is different, and there typically the first author is the one that did most of the work. In such fields the first author position is the most prestigious one. The last author typically has a role more on the background, for example by posing the research project and/or playing an advising role.

I have never heard of any convetion where the supervisor is the first author if they didn't do the majority of the work.