At what time in the Apollo 14 mission did the maneuver shown in this image happen, and what exactly was happening?

Question

In a search for information for this answer I received this google books link of Comment: The Relevance of Space, by Arthur Kantrowitz, Bulletin of the Atomic Scientists 197, 4 April 1971, pp 32-33. It includes the image below, I've retyped the caption for easier reading.

At roughly what time in the Apollo 14 mission was this, and what does "capsule separating from the S4B" really mean in terms of the "unpacking of Apollo" sequence that Walter Cronkite explained on TV holding those models in front of the camera years ago but I still can't quite understand?

Apollo 14 (at arrow tip) is nothing more than a speck in the sky at 40,000 miles from Earth. This picture of the spacecraft was taken by Justus Dunlap of Northwestern University’s Corralitos Observatory, and shows the capsule separating from the S4B rocket. The capsule itself is visible as a pinpoint at the apex of the fan and the fan itself is expanding rocket exhaust.

Answer 1

The S-IVB was the third stage of the Saturn V rocket, which took astronauts to the moon.

The S-IVB ignited its engines in the upper atmosphere, to push the rocket into low Earth orbit, where it would sit for a few hours as the crew prepared for the trans-lunar injection (burning towards the moon so that they can leave the Earth).

After performing that burn, the S-IVB would no longer be needed, so the command module separated from it. After separating, the command module would turn around and grab the lunar module, which was stored in the top of the S-IVB.

This video has a good explanation of the whole mission, and the specific part you're talking about is at 2:30.

According to the timeline for events of the Apollo 14 mission (history.nasa.gov), the command and service modules separated from the S-IVB at 3:02:29.4 after launch, which was about 28 minutes after the trans-lunar injection burn.