Advanced form of age-related macular degeneration (AMD) is a major health burden that can lead to irreversible vision loss in the elderly population. The early signs of AMD are drusen, which appear as yellowish deposits under the retina. The end-stages of AMD include two forms: wet AMD (neovascular) and geographic atrophy (GA, non-neovascular). We propose a deep learning approach using a pre-trained VGG-19 neural network to classify the optical coherence tomography (OCT) images into wet AMD, GA, drusen, and healthy images. To explain the results, we quantify and present the prediction confidence and reliability as well as the regions of interest deemed to be important by the deep learning model when classifying OCT images. The sensitivity of classification for wet AMD, GA, drusen, and healthy images was 91.67%, 88.00%, 96.30% and 100% respectively, with the most confident predictions being for the drusen and healthy images. Visual inspection of the misclassified images using heatmaps using the Gradient-weighted Class Activation Mapping (Grad-CAM) algorithm revealed that, for most of the misclassified images that had high prediction confidence, the algorithm identified correctly more than one region of interest, each belonging to a different AMD category. We concluded that, rather than assigning just one label to an AMD image, algorithms for AMD classification should allow multi-labels as images generally show evidence of more than one stage of AMD simultaneously (e.g., drusen as the predominant region and GA as a small region of interest).