As so often with basic measurements like this, the roots have been laid out way before today's computers, even before computers (non human that is) at all.
From what I read, most line printers have 132 columns. Also, the VT-220 and presumably other terminals may be switched between 80 columns (that's a usual width) and 132 columns.
The number is a result of the paper originally used for tabulating machines and a common font size at some later point. In this case it's 14 inch wide paper and a 10 characters per inch printing, which resulted in 132 characters per line - the remaining 8 character positions are omitted for the transport tractor feed pin holes.
But what's special about 132? It's hardly more than 128, which has the advantage of being a power of 2.
As being developed way before the binary computer, powers of two are not related in any way.
It's about the paper.
It begins with tabulating typewriters. Most notably they carry a quite wide carriage able to hold paper of 22 or sometimes more inches wide. Classic (pre-computer *1) ledger sheet size (in the US *2,3) is 22 inches wide (*4). To place tabulating machines into accounting business, similar forms had to be used.
Long story short(*5), the result was support for 10 characters per inch and 6 or 8 lines per inch, and a two paper formats based on a 'half ledger' of 11 inch:
- 8.5 x 11 inch with 80 characters per line and 66/88 lines per page
- 14 x 11 inch with 132 characters per line and 66/88 Lines per page
plus a (later) 'condensed' format of
- 14 x 8.5 inch with 132 characters and 66 lines per page (only 8 lines per inch)
When computers came along, their printers were not only built using the same components as tabulating printers, but more importantly had to adhere to these paper formats to be useful.
Minis (as the mentioned VT terminals) and micros just carried it on - again to make their output useful to the businesses they where meant to be sold to.
*1 - Classic as in genuine handwritten thread-bound ledger books.
*2 - Jup, that's the sheet size where the ledger page size comes from.
*3 - European pre-DIN formats were similar, which opens the interesting notion that the printing press was already setting international standards way before any standardization organization. Just not as systematic.
*4 - Or better most used was 17" x 22". Other common ledger sizes are, 17" x 28", 19" x 24", 24" x 38"
*5 - There was much variation of character density and capability among early machines. For example a IBM 405 only handled 8 character per inch and a total of 88 print bars (positions). At least it could also print letters, where the earlier 285 could only handle numbers.