The ram is the great animal of substitution and sacrifice. In the Book of Genesis, when Abraham is commanded to sacrifice his son Isaac and then stayed at the last moment, he finds a ram caught by its horns in a thicket and offers it in the boy's place, a scene of the sacrifice that is provided instead, central to Jewish, Christian and Islamic memory. The ram's horn itself becomes an instrument of the sacred: the shofar, sounded in the synagogue at the new year and the Day of Atonement, is a ram's horn, its call a summons to repentance. As Aries the Ram it opens the zodiac. Creation, kingship, sacrifice and the summons to God gather to the horned male sheep.
A technical point is worth adding to the zodiacal reference above: the sign of Aries and the constellation Aries are no longer the same patch of sky. Because of the earth's slow axial precession, the position of the vernal equinox, which tropical astrology fixes at zero degrees Aries, has drifted since antiquity and now actually lies within the constellation Pisces, a roughly two-thousand-year drift that sidereal systems of astrology account for and that tropical systems, by definition, do not. Most halakhic authorities require the shofar specifically to be a ram's horn rather than any kosher animal's, and one horn is explicitly ruled out regardless of the holiday: a cow's or an ox's, disqualified because it would recall the sin of the Golden Calf, the Talmudic principle being that an accuser cannot also serve as a defender.