Gravity is the force that connects every object - planet, the Sun, moons, asteriods, comets - to every other object. The Earth is constantly being tugged by all the other bodies in the solar system. Except for the Sun and the Moon, most bodies are either too small or too far away to have a noticable effect. We are bound to revolve around the Sun due to the Sun's gravitational pull on us. The Moon affects our tides and the rate at which we spin. Slowly over the centuries the Moon is acting like a brake to slow down our days. The dinosaurs had 18 hour days! We affect other bodies too. We pull other small objects towards us so we occasionally have meteors crash into us.
Among all the celestial bodies, the sun impacts the earth maximum. It provides the earth with large amount of heat and light energy. Relative motion of earth with respect to sun cause the daily cycle of day and night and annual cycle of seasons.
After sun, the celestial body having maximum impact on the earth is the Moon. It is quite small as compared to earth and other celestial body. But because of its nearness to earth it exerts major gravitational force on earth causing the cycle of high and low tides. Also though the moon is not luminous, provides some illumination to earth at nights by reflecting the sun rays falling on it. Because of the relative movements of moon, earth and the sun, and their position relative to each other, the amount of light reflected from it on to the earth varies in a cyclic manner. The moon also causes solar eclipses. The total effect of solar eclipses on the earth is not completely understood, it is established that it causes some radiations to that have subtle impact on plants and animals on earth.