The honest answer is: both secret and private — and understanding the distinction matters.
A private society is one that does not publish its proceedings, does not seek public membership drives, and conducts its affairs behind closed doors. The Rotary Club is private. Your local chamber of commerce is private. They do not hide their existence; they simply control access to their meetings.
A secret society is one whose very existence may be concealed, whose members deny their affiliation, and whose purposes are hidden from the world. Freemasonry is not this — not anymore, and not entirely. The lodge does not hide its buildings. It does not deny its charitable work. It does not conceal its existence from the public square.
But Freemasonry is secret in what it promises to keep secret: the modes of recognition, the rituals of initiation, and the obligations taken at the altar. These are not hidden because they are shameful. They are hidden because they are sacred. A man does not whisper the secrets of the lodge because he fears persecution; he whispers them because he has promised to do so, and his word is his bond.
This duality has defined the Craft since its inception. In 1737, when the Catholic Church issued its first papal bull against Freemasonry, the lodge did not disband. It did not go underground. It simply closed its doors more firmly and continued its work in the light of its own lamps. The world knew where the lodges met. What happened inside remained — as it remains today — the private property of those who have earned the right to know.