The golden hour occurs around sunset and sunrise.
Its duration is not exactly an hour and depends on location and date. Typically, it lasts between 30 mins (usually in the winter when days are shorter) and 2 hours (usually in the summer when days are longer). However, close to poles it may not happen, or it may last much longer when it is close to a solstice.
There may not be an exact definition, although I use Civil Twilight for my calculations based on experience. The main point is that during that time the brightness of the sky should balance with the reflectance of naturally illuminated objects. In other words, during the golden hour, the contrast between foreground and background (sky) is lowest. This is precisely why it is important in photography since this lets the most details be captured throughout a scene.
The second half of the morning and first half of the evening golden hour is characterized by warm light (golden) which is a result of the low angle of illumination of the sun. This is where its English name comes from.
The French, call it L'Heure Bleu which means Blue Hour from the first half of the morning and second half of the evening of the golden hour which is characterized by a deep blue sky resulting from indirect illumination of the atmosphere. It is more pronounced in the East in the morning and in the West in the evening.