Most people are aware of their Sun sign and some who look a bit more deeply, are aware of their Moon sign as well. An interesting thing to take into account is your Secondary Placements. Technically, all of the signs have Ruling Planets and you can uncover underline influences behind all placements by traversing a chart more intricately, but the Sun & Moon are universally the rulers of Leo and Cancer exclusively which is why they are the easiest to look to first. For example, if you are a Sun in Libra, but have Leo in the Third House of your birth chart, you will exhibit a stronger sense of yourself when in relationships and your community (through communication); this also would mean that (in most cases) Cancer would be in your Second House giving you qualities of a lunar Taurus, despite the fact that your Moon would likely be in Virgo (depending on the exact degree) for this particular example.
I have come across charts where the Moon is sitting in the Second House in Virgo, but Cancer is sitting in the 12th House, which would create a very mentally complex and systematic individual with an attachment to physical objects. Other charts I have observed had an individual with Moon in the 10th House and Cancer in the 5th House, which instills a desire to feel successful doing something that is both pleasurable and enjoyable.
Learning more about the intricacies of the planets metaphorically relate to your personality is an interesting way to get outside of the instinctive bubble we tend to view ourselves through, which is usually an old story about ourselves forged in childhood (sometimes good and sometimes bad). I can relate to my own Secondary Placements, and they help me understand my inner instincts and egotistical reactions.