The Earth's equator projects to the celestial equator, thus the name. The coordinates of stars and other 'fixed' objects change only very slowly in this coordinate system, so it is ideal for cataloging sky objects. The ecliptic is a great circle, inclined about 23 degrees to the celestial equator, on which the Sun is always found. The Sun goes through the thirteen constellations intersected by the ecliptic called the Zodiac. Most objects also orbiting the Sun are inclined to the ecliptic by less than a few degrees, therefore ecliptic coordinates are easily calculated for planetary orbits.
Ecliptic longitude is abbreviated 'lamda' and ecliptic latitude is 'beta'.
Horizonal coordinates are also known as alt-az coordinates. They describe the altitude above the horizon and the azimuth, that is the compass direction in degrees. These coordinates are very useful if you want to find something in the sky. They change however, according to the location and time of the observation, so the time, date, longitude and latitude are required to calculate horizonal coordinates. In addition to the chart like display, this program can also calculate the positions of planets and the sun and moon.