Merrily did we drop below the kirk

As the ship sailed further from shore first the church, then the hill, then the highest point of the lighthouse fell out of sight (because of the curve of the earth). Of course, at the same time the ship ceased to be visible from the shore.

This is a poetic metaphor, and not to be confused with the modern drop out of sight which means either literally to fall to the ground deliberately so as not to be seen, as soldiers and wild animals do, or metaphorically to cease to go out (perhaps simply by staying at home), so that those searching for you, whether police or others, cannot find you.

Departing ships appear to sink beneath the horizon thanks to the curvature of the Earth. When someone sees that happen depends on how far they are from shore and how high they are above sea level.

Kirk is an old Scottish word for church. Churches, with their high steeples, oftentimes were the tallest structures in town. Someone at the top of the steeple would be the last person in town to see a departing ship disappear over the horizon. If the town had a nearby hill, someone at the top of that hill would see the departing ship disappear over the horizon after the person at the top of the church steeple saw the ship disappear.

Finally, suppose there's a spit of land near the town that sticks far out to sea. People built tall lighthouses on those spits of land to warn ships of the danger. Someone at the top the lighthouse would be the last to see the ship sink beneath the horizon.