Because the points are not like pixels in a continuous space, pointnet first sample a few anchors from the point set. Then every anchor point will find their k nearest neighbor(like CNN works on windows of pixels). Then with shared MLP layers, point will now have higher dimension of latent features. Last, to aggregate features of local points, max-pooling will used on every group of points that we clustered previously.

This is one layer they called Set Abstraction layer. Which repeat for 4 times. After SA layers, Feature Propagation Layers can be used if ur task is segmentation, which just upsampling the points.