Why Low Frequency called Approximation and High Frequency Detail?
Intuitively speaking, anything that is 'high frequency' is something that is 'rapidly changing in time'. Anything that is 'low frequency' is something that is 'slowly changing in time'.

If you think about it, any time you have 'detail' in a signal or image, it means that you have, very quick, rapid variations in time or space. This then becomes the 'detail' of your signal/image. 

In contrast, if you just care about how something changes generally, you care about long-term trends - you dont care about how things change with every sample, you just care about how things change over a long time, or over long space. In this case, you just want to 'approximate' your signal.