What is the point of octave? (And its presumed buddy, MatLab)

I installed octave, since I saw mention of it here and there, and it's
purported similarities to MatLab.

Well, now that I have it, my fundamental question is: What do I do with
it?

Consider that I am using Maxima extensively now, and have used
Mathematica extensively in the past. They are obviously largely
symbolic algebra systems. I can do differentiation, integration,
various matrix equations, oodles and oodles of functions (such as
"laplace()"), systems of equations, etc. etc. etc. I'm sure everybody
here knows that.

But reviewing the Octave primer and Octave reference manual, I haven't
really figured out its overall purpose. It sure doesn't seem to be
symbolic at all. Is it numerical only? So equations would have to be
"solved" in something like Maxima first?

Is it primarily for interfacing from programs I write? What problem
exactly is it supposed to solve?

Thanks!
David Logan

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