The CSS 3 specification is clearer:
This property indicates the desired height of glyphs from the font. For scalable fonts, the font-size is a scale factor applied to the EM unit of the font. (Note that certain glyphs may bleed outside their EM box.) For non-scalable fonts, the font-size is converted into absolute units and matched against the declared font-size of the font, using the same absolute coordinate space for both of the matched values.
You asked:
what I have found, in some accepted answers (in stackoverflow), statements being the height of capital 'H' otherss of capital 'I' and lower 'p' plus some amount.
It depends on the font. The CSS can only describe the desired height of the em box, but the font author can draw the glyphs anywhere they like inside or outside it. See here for more details.
I am interested in that to know how this metrics relate to monospace typeface's character width.
Only indirectly. Different monospace fonts have different ratios between their height and width.