It's supposed to mean that at your core you are Cancer--sensitive, gentle, complex, and broody, but your outer appearance (and strong influence) is Aries. I'm an Aries ascendant, and it really helps to balance my less assertive Pisces side.
Aries ascendant is supposed to be a very strong ascendant, making a person more of a leader, more assertive, active, and people-oriented. It is supposed to enhance your willpower and drive for achievement.
The third strong influence is supposed to be your moon position.
Joanna Martine Woolfolk, "The Only Astrology Book You'll Ever Need."