I've seen that « ça veut dire » means "it means", however, I'm wondering about the exact feeling of the phrase. It is more like "that is to say" or "in other words"?
There isn't really such a thing as one right translation for every scenario. The context would determine the exact phrasing, as well as the type of logical connection suggested by the phrasing.
All of the above are fine, as well as "That implies" or "That's no different than" or any number of equivalent expressions. "That means" is a very good catch-all that fits most scenarios.
« On se rend compte que les circonstances ne s'avèrent pas idéales. » Ça veut dire qu'on est foutu.
"We are cognizant of the fact that circumstances cannot be called ideal." That means we're screwed.
Selon Aristote, les humains ont le cerveau très humide. Je ne sais pas ce que ça veut dire.
Aristotle says humans have very moist brains. I'm not sure what that means.