It can be a few different things, depending on which field of philosophy one practices and in what context – but by and large, most philosophy is done within academia. For me, and in most of the writings I’ve read by my fellow philosophy grad students, it mostly means reading other (mostly male and dead) philosophers and then writing about their ideas. I make greatest use of the compare/contrast—> synthesize/speculate method, which is (frustratingly, to many) heavily relied upon in Continental philosophy. The only field of philosophy I have explored that is unlike this is logic, which is refreshingly math-like.
So I guess that philosophizing can be thought of as having an opinion – and it certainly is, in some cases – but I’d say it’s more like having a hypothesis. The papers I write do sometimes end up contradicting that hypothesis, as in the course of writing them I often come to see things in a different way. It’s kind of like those science reports we all had to write back in high school – you make a guess, and if your results end up not bearing out the guess, that’s ok but you have to state it in your conclusion.