What is intended by a spiral on a character's finger and what is the origin of this trope?
As mentioned before, it's a fingerprint.

Usually the spiral only appears when the character's finger/thumb is close to the screen. The reason for this is simply to add detail to something which is taking up a lot of the screen. Look at the image without the spiral:




Because the finger takes up a lot of the screen it's harder to focus on when it's all the same colour. The inclusion of the fingerprint helps break up that space - even if it is a basic design.

The reason it's a spiral is for simplicity's sake. Fingerprints are very intricate and are more trouble that it's worth, unless perhaps the entire animation is ridiculously detailed - otherwise you would get a sharp jarring contrast between the foreground and background:



Obviously, this is exaggerated, but I imagine half-hearted attempts would also look out of place.


  If there's a spiral on her finger when she points at you, she's being triumphant or prideful.


I don't think there's any real evidence to suggest this. This design is used in many situations, often when a character is angry.

TL;DR - It's to break up the area on the finger without going into much detail