Three different questions
Your Sun answers “what are you here to become?” It’s your sense of direction and what you’d like to be proud of. It’s also the one placement you get from your birthday alone, in almost every case.
Your Moon answers “what do you need?” It’s your emotional habits: what soothes you, what sets you off, what you do when you think nobody’s watching. You often can’t see it from across a room.
Your Rising, or Ascendant, answers “how do you come across?” It’s the sign that was on the eastern horizon when you were born, and it describes your manner, your first impression, the front door of the house.
A simple way to hold them in mind: your Rising is what people meet, your Sun is what they get to know, and your Moon is what they find out once they’ve seen you tired.
When they agree, and when they don’t
Most people have three different signs here, and that’s where the interest lies. Take someone with a Capricorn Sun, a Cancer Moon and a Gemini Rising. At a party they chat and seem to know everyone. At work they’re hugely reliable and quietly ambitious. At home they need the people they love close by, and they get hurt more easily than anyone would guess.
Their friends may disagree about what they’re like, and all of them are right. That’s a useful thing about the Big 3: it explains why you can feel misread. If you’re tired of being told you seem calm when you’re falling apart, you may simply have a calm Rising over a stormy Moon.
When two of the three share a sign, that theme tends to get louder. If all three match, what you see is largely what you get, and the person’s habits are often very clear to them and to everyone else.
Why dating profiles benefit from them
Every MatchMachine profile shows Sun, Moon and Rising, when they’re known. Your exact birth data stays on the server. Rising needs a known birth time, so without one it stays off your profile. There’s more on that in why Rising needs a birth time.
Three signs make for a better opening line than one. “Your Moon’s in Scorpio, should I be nervous?” is a nicer start than “hey,” and it invites a real answer.
What they don’t tell you
The Big 3 are a good sketch, and that’s all. Comparing them with someone’s doesn’t tell you how you’ll get along. For that you’d compare whole charts, which is what synastry does. The app’s reports go further into your own combination. To start exploring on your own, try the Sun and Moon combinations and the Rising signs.