Half a byte (4 bits) is a nybble. The joke is so awful that it stuck. A nybble can store a single decimal digit; when this is done for many digits, the result is BCD.
One hex digit describes precisely one nybble. Thus, anyone writing hex strings is really writing down nybbles. And any BCD is immediately recognizable in hex -- just read the hex digits (which are all 0,...,9) as decimal.
The most modern machine I know of that uses nybbles is the HP48 (and, presumably, the HP49, not to mention the alphabet soup you can write after either name). The Saturn processor used internally, and the internal RPL, both seem to be heavily oriented towards nybbles. Apparently Saturn is something of a 4 bit CPU!