Vantage Points are always high up, so you need to look around for a way to climb up. Once you reach the vantage point there is a special marker where you can press R3 and see a picture of how things used to be in the 'old days'. Also an associated audio recording. There is also a supply box nearby.
There is a trophy for finding your first vantage point and another for finding all 12 of them. You get a skill point for each set of four you collect.
Some merchants sell maps which will mark all the locations on the map.
In addition to the audio that you can play when you find the vantage point there is also a longer story in the entries for the vantage point in the Notebook. This story reveals how and why they exist.