VGG16 and VGG19 have been introduced in Very Deep Convolutional Networks for Large Scale Image Recognition, Karen Simonyan, Andrew Zisserman, 2014, https://arxiv.org/abs/1409.1556. The network used 3×3 convolutional layers stacked and alternated with max pooling, two 4096 fully-connected layers, followed by a softmax classifier. The 16 and 19 stand for the number of weight layers in the network (columns D and E):
An example of very deep network configurations as seen in https://arxiv.org/pdf/1409.1556.pdf
In 2015, having 16 or 19 layers was enough to consider the network deep, while today (2017) we arrive at hundreds of layers. Note that VGG networks are very slow to train and they require large weight space due to the depth and the number of fully-connected layers at the end.