What is meant by PCA preserving only large pairwise distances?
If I can re-phrase @Don Reba's comment:
The PCA transformation itself does not alter distances.
The 2-dimensional plot often used to visualise the PCA results takes into account only two dimensions, disregards all the other dimensions, and as such this visualisation provides a distorted representation of distances.
I am currently reading up on t-SNE visualization technique and it was mentioned that one of the drawback of using PCA for visualizing high dimension data is that it only preserves large  pairwise distances between the points. Meaning points which are far apart in high dimension would also appear far apart in low dimensions but other than that all other points distances get screwed up. 
Could someone help me understand why is that and what does it mean graphically?. 
Thanks a lot!