You would use Octave instead of Matlab because it is free as opposed to $1000 for a basic license plus additional $$ for every time you sneeze and need a toolbox.

You would use Octave/ Matlab instead of Julia, R or Python because Matlab syntax is the cleanest and most succinct way currently to articulate complex (in both senses) matrix algorithms. It isn't nearly as good for general programming, but it is much better than anything else for its niche. While some of that is obviously just fuzzy opinion, I am pretty sure you need fewer characters or LOC to say the same thing in Matlab than in the other scientific languages mentioned.

Matlab (and thus Octave) also has a HUGE installed base of engineers who don't really care that HN thinks the language du jour is X, Y, or Z and continue to use Matlab to get their work done (and will for the next 20 years). If you are working with them, you use Matlab. If you are working with them and don't have $1000 for a license, you use Octave.

Octave also has some syntactical improvements like "+=" that are missing in Matlab.