As I write this, the planet Mercury is in transit across the Sun, I know this because I just watched a live feed of the event on Youtube.
(I don’t have a suitable solar filter for my telescope, or I would have set up and watched it myself!). A transit is, of course, just another name for an eclipse. The planet is passing between us and the Sun, a purely geometrical effect; it is a result of where the Sun, Mercury, and the Earth all are, and how they are moving. What you can see from here is a tiny black dot moving slowly across the face of the Sun. It takes several hours. Transits have no inherent significance, but astronomers do observe them because it allows them to make precise timings of planetary orbits, useful for testing Newtonian mechanics and General Relativity.
It is also possible to observe transits of extrasolar planets as they move between us and their parent star. Since no stellar nor planetary discs of any kind can be resolved at interstellar distances, what we measure is the very slight winking of the star’s light as the planet crosses in front of it. This is right at the limit of our technology–and it helps if the star is small, and the planet is big, that is, the eclipsed patch of star is large compared to its glowing surface.. The ideal case would be a gas giant planet eclipsing a dwarf star. Of course, the geometry has to be just right, too; if the Earth is not in the orbital plane of the system, no transit observation would be possible; the planet would appear to pass above or below the star. Still, this method has been used to confirm the existence of extrasolar planets, even though it is not capable of revealing all of them.
It is also important to keep in mind that just because we are in the orbital plane of the extrasolar planet, that does not mean an observer on that world would also be in the orbital plane of ours. If there are alien astronomers surveying their skies for transits, then they would only see these transits if their home star happened to be in the plane of our system. This plane is marked on our star charts by the ecliptic, the line through our skies that marks our sun’s yearly path around the sky, and which our own planets always seem to be near. The constellations that cluster around the ecliptic are the zodiac, to use the astrological term.
It has also been suggested that alien astronomers located on our ecliptic using transit observations would likely know there were planets around Sol, so they might find it worthwhile to signal in our direction just to see if anyone was home. Therefore, that might be a good place for our own SETI researchers to concentrate on. That’s a lot of assumptions there, and many based on pure selection effects, not any physical realities, but it is a thought.