A solar eclipse is the Moon hiding the Sun. A lunar eclipse is the Moon entering Earth’s shadow. Both happen when the Sun, Earth and Moon fall into a straight line: a solar eclipse at new moon, when the Moon passes between the Sun and Earth, and a lunar eclipse at full moon, when Earth passes between the Sun and the Moon. This page runs all three bodies on their real periods so you can see what happens as the line comes together.
New and full moons come around every 29.53 days, but eclipses do not follow every one of them. The Moon’s orbit is tilted 5.145 degrees from the plane of Earth’s orbit, so at most new moons the Moon passes a little above or below the Sun, and at most full moons it passes above or below Earth’s shadow. Turn the orbital tilt off in the display panel and you can confirm that without it an eclipse would arrive every month.
An eclipse needs a new or full moon near one of the nodes, the line where the Moon’s orbit crosses the plane of Earth’s orbit. That window is called an eclipse season. It comes around about twice a year and lasts about 34 days. The nodes themselves drift, taking 18.6 years to travel once around to the west, so each eclipse season arrives a little earlier than the last and never settles into the same time of year.
Choosing the solar or lunar scene lines the nodes up so that the eclipse is certain to happen, then starts the clock a little before it. You get the approach, the alignment, and the parting in one continuous run. The speed is set in the display panel, and the default of 0.06 days per second covers roughly an hour and a half of real time every second.
The corner at the lower left shows the Moon as seen from Earth. In the phases scene it runs through the whole cycle; during a lunar eclipse you can watch Earth’s shadow cross the face of the Moon. During a solar eclipse the Moon is on the Sun’s side, so the view there stays close to a new moon.
The sizes and distances are chosen to be readable, not to scale. The Sun is about twelve thousand Earth diameters away, and at that scale both Earth and the Moon would be single points on the screen. The periods and the tilts are the real values, so the question of when an eclipse happens is answered correctly even though the picture is not.