A "half-rack" is simply a form factor for audio equipment units.
For example, you can have an effects unit that sits in a rack for
protection, a "full-rack" is an effects unit (or amp, or whatever)
is twice as thick as a "half-rack".
So if you can fit 4 full-rack units in a rack, then you can fit
8 or so half-rack units in that same rack (but leave room between
the units for airflow).