You dont have to be fully into GR to know this. Just do any sphere shit and you should see it.
Imagine you have a vector on the North pole, pointing towards the South pole passing through x=0 line. If you move this vector down to the equator, it will be pointing the straight towards the South pole. Then you parallel transport it to the y=0 line via the equator, it will be pointing still straight towards the South pole. Now you transport it back up to the North pole, and you realise you have a 90 degree rotation of the original vector