A common method for building walls is to use vertical studs (often the classic "2x4"s) to support the surfaces of the wall:
The standard spacing for these studs is 16 inches "on center", which means that the stud centers are 16" apart. This provides a good balance between strength and expense. 16" is also a common spacing for other building supports (beams and joists).
The tutorial is describing building an additional surface to block the sound, supported by studs. However, this wall will be supported by studs every 24" rather than every 16". I'm guessing the wider spacing is for two reasons:
- Loosen the support of this new surface, so that its vibrations won't be directly transmitted into the main wall and thus into the "quiet" space
- Reduced cost