Why might a craft or other three-dimensional object, such as an african mask or fine porcelain, not be understood as an isolated piece in a museum? how might people gain a deeper insight into these objects?

African masks which weren't made for the tourist trade are religious objects and were made for certain ceremonies. Without knowing something about the culture and purpose for which the mask was made it can not be understood.
Not sure about fine porcelain, except that it may have meant to be used or it may have meant for display.

It increased the value of original works of art.