Being born on the “cusp” simply means that you were born on the day that the Sun changes signs. So often, those who were born on an astrological “cusp date” will say, and often believe, that their personality seems to contain the qualities of both Sun Signs. For example, a person born on January 20th may feel that they behave at times like a Capricorn and at other times like an Aquarian exhibiting traits of both signs.
In my extensive and varied personal experience as a professional astrologer, I am certain that this is simply not true. In every single instance, without exception, the person who believes that they conduct themselves in a manner which is a blend of both “cusp Sun Signs” is behaving in that manner because that person’s Moon, Ascendant, or personal planets are the “second” sign. For instance, if a person was born on January 20th in the morning of that day (depending on the year) they are a Capricorn Sun Sign, and if said person has other planets in Aquarius in their chart would be incredibly common seeing that the inner planets often travel closely together.