What did the Apollo rocket do while the lunar module was directed toward the moon's surface?

If you mean while the Lunar modules were descending to the surface and while they were on the moon, then the Apollo Command and Service Modules kept orbiting the moon. One of the astronauts stayed behind in it. The Command Module could relay messages from the earth to the astronauts on the lunar surface. The ascent stage of the Lunar Module eventually returned and docked at the forward end of the Command Module.

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