Which TrueType font table stores information about the actual character layout. That is, the size in pixels or points with which the symbol is displayed on the monitor.
For reference: I am working with font tables using the fontTools library.
Glyphs' heights are not specified anywhere (at least, not for a horizontal layout). Probably, what you're looking for is sxHeight from the 'OS/2' table (the distance between the baseline and the approximate height of non-ascending lowercase letters). There's also sxCapHeight field (for uppercase letters). Though, those fields were defined in the second version of the OS/2 table.
To find out the glyph's height, you can simply subtract its lowest point from the highest one (i.e. glyph height = yMax - yMin). yMax and yMin are stored in Glyph Header in the 'glyf' table (for TrueType outlines).
If you need glyphs' widths, 'hmtx' table contains an advance width for every glyph in a font, as well as left-side bearing (right-side bearing is not stored, when needed it has to be computed from left-side-bearing + maxX - minX). 'hhea' table contains a maximum advance width value (advanceWidthMax).