Summary
Secret Levels, just like normal levels, award items and stars upon completion. However, as their name suggests, they are hidden in secret locations on the World Map and only show up when tapped.
List of Secret Levels
1 Hidden Quattuor on ruins
2 Hidden Peacats on bird bath
3 The Secret Field on purple tree
4 Blessing Caves on big boulder
5 Hidden Mountain on yellow tree
6 Hidden Blessings on grave
7 The Hidden Reef on green fruit bush
8 Hidden Shrine on stump
9 Hidden Lake on lovely potted flowers
10 Hidden Ytu Plains on statue.