They are not necessary to write a program, but you will very soon discover just how essential they are to maintain the program

Yes, They should clarify the action of the section of code;
There is no point in simply commenting the function of, say, the ADD instruction - that can simply be found from the data sheet.
It might be worth commenting if you rely on some obscure side-effect, but generally your comments should explain things like the reason for needing to do the particular addition at this particular point

Variable definitions should be commented to say what the variable means; eg what units does the value represent?
There's a famous case of a NASA space probe which was lost because one part of the software assumed a variable was in inches, but another assumed millimetres!