In order to *generalize* to various tasks in the wild, robotic agents will need a suitable representation (i.e., vision network) that enables the robot to predict optimal actions given high dimensional vision inputs. However, learning such a representation requires an extreme amount of diverse training data, which is prohibitively expensive to collect on a real robot. How can we overcome this problem? Instead of collecting more robot data, this paper proposes using internet-scale, human videos to extract "affordances," both at the environment and agent level, and distill them into a pre-trained representation. We present a simple framework for pre-training representations on hand, object, and contact "affordance labels" that highlight relevant objects in images and how to interact with them. These affordances are automatically extracted from human video data (with the help of off-the-shelf computer vision modules) and used to fine-tune existing representations. Our approach can efficiently fine-tune *any* existing representation, and results in models with stronger downstream robotic performance across the board. We experimentally demonstrate (using 3000+ robot trials) that this affordance pre-training scheme boosts performance by a minimum of 15% on 5 real-world tasks, which consider three diverse robot morphologies (including a dexterous hand). Unlike prior works in the space, these representations improve performance across 3 different camera views. Quantitatively, we find that our approach leads to higher levels of generalization in out-of-distribution settings. For code, weights, and data check: https://hrp-robot.github.io