The object is to get the 4 green dots to the upper right corner. The blue dots to the bottom right corner, etc.
See the red triangle in the top left corner? Tap on that and those 8 dots will rotate in a loop. Tap on one of the bottom triangles and those rectangular loops will rotate.
Spin Dots is hard! I've solved it twice.
There is a mechanical version that is similar: The Orb, which I really like.
Spin Dots is a free puzzle app game. Can you do it?