Short answer: Golden hour in photography is the time briefly after sunrise or before sunset when the sun is low in the sky and the light is orange/red.

What Causes Golden Hour
When the sun is low in the sky it has to travel through more of the earth’s atmosphere in order to reach you, rather than beaming straight down as it does during the day. As the white light travels through the atmosphere the colours with shorter wavelengths, like blue and green are scattered leaving behind the red and orange end of the spectrum. This is why the light we see is orange/red.
Resource: Wikipedia.
Is It Exactly An Hour?
No, the term is used purely to indicate a short amount of time close to sunrise or sunset. People just use the golden hour as a way to refer to a time when the light is more orange than typical daylight and a good time for taking photos.
Take Advantage of It
The golden hour is absolutely something you should keep in mind if you like the aesthetic. In general, shadows are not as harsh and highlights will not be as bright. In general your images should have less dynamic range than a clear day and will have a warm feel.
Golden Hour Sample Galley
Check out some photos I’ve taken during golden hour. As always, these photos are free to use with an image credit.
Short Video Introduction
Here’s a short 2 minute introduction to the topic from Dean Rojas on YouTube:
Longer Video on Golden Hour
Check out this video from Channel 8 on YouTube for a more in depth dive into the topic, including what causes the golden hour and shooting tips: