It often happens that two or more similar values are distinguished with the
' symbol, e.g.
a, a', a'' and similar. How is this pronounced?
As @waiwai933 said, the answer is A prime, A double prime, ans so on. As usual, Wikipedia has more details. In French (and probably other languages), double prime, triple prime, and so on are named seconde (2nd), tierce (an old word for 3rd). According to wikipedia, it was the same in English before the 1960s (but the relevant sentence is tagged with ).
This progression is indeed the etymological origin of the symbol, which was initially a superscript Roman number.
I encountered this ' in the context of vector math referred to as a dash in the book Support Vector Machines which you can read about at http://www.support-vector.net/nello.html published by Cambridge University press. I have never encountered this usage before. The use is in the math appendix, example B-2.
"We use a dash to denote transposition of vectors (and matrices) so that a general column vector can be written as..."
We read a' as "a dash" in Japan. However, "a prime" is occasionally used in universities. At its explanation of the word prime, the Oxford English Dictionary VIII (1970) states that a' is "usually read 'a dash', etc." I think the tendency that "dash" is changed to "prime" is caused by LaTeX (or troff), which is used from 1980s and in which a' is formatted as