Final answer:
Mars' orbit is close to the ecliptic because the solar system is flat with planets orbiting in nearly identical planes, and Mars exists within this alignment. The ecliptic's relevance to eclipses is due to the Moon's orbit intersecting it, enabling solar and lunar eclipses.
Step-by-step explanation:
The orbit of Mars never takes it far from the ecliptic because the solar system is rather flat, and all the major parts, including planets, move in nearly the same plane. The ecliptic is the path the Sun appears to take against the background stars as seen from Earth. All the planets, including Mars, orbit the Sun in this same general plane. Mars has an elliptical orbit around the Sun with an eccentricity of about 0.1, but it remains close to the ecliptic due to the aligned orbital planes of the planets in our solar system.
The term ecliptic also relates to eclipses. Eclipses occur when the Moon's orbit, which intersects the ecliptic at about a 5-degree angle, allows the Moon or Earth to cast a shadow causing a solar or lunar eclipse.
Overall, the commonality of the orbital planes for celestial bodies leads to their paths being aligned within an 18-degree-wide belt in the sky, known as the zodiac.