What is the meaning of hand crafted features in computer vision problems?
"Hand Crafted" features refer to properties derived using various algorithms using the information present in the image itself. For example, two simple features that can be extracted from images are edges and corners. A basic edge detector algorithm works by finding areas where the image intensity "suddenly" changes. To understand that we need to remember that a typical image is nothing but a 2D matrix (or multiple matrices or tensor or n-dimensional array, when you have multiple channels like Red, Green, Blue, etc). In the case of an 8-bit gray-scale image (or a "black and white" image, although this latter definition is not quite accurate) the image is typically a 2D matrix with values ranging from 0 to 255, with 0 being completely black and 255 being completely white. Now imagine an image of a blackboard set against a totally white wall. As we move left-to-right in the image the values in one of the rows of the matrix might look like 255-255-255... since we will be "moving" along the wall. However, when we are about to hit the blackboard in the image it might look like 255-255-0-0-0...As you might have guessed, the blackboard "begins" in the image where the zeros start. In other words, the "intensity" of the image along the "x" axis has dropped rather suddenly (or a very large negative gradient along x), which means a typical edge detector will consider it to be a good candidate for an edge. 

The algorithm that we just saw is only the very basic of algorithms, and others like Harris corners and Hogg detectors use slightly more "sophisticated" algorithms. Actually, even the Canny edge detector does a lot more than I what I just described, but that is besides the point. The point is that once you understand that an image is nothing more than a data matrix, or an n-dimensional array, the other algorithms are not that difficult to understand either.

As regards your last question: 


  Is this related to learned features?


The "handcrafted features" were commonly used with "traditional" machine learning approaches for object recognition and computer vision like Support Vector Machines, for instance. However, "newer" approaches like convolutional neural networks typically do not have to be supplied with such hand-crafted features, as they are able to "learn" the features from the image data. Or to paraphrase Geoff Hinton, such feature extraction techniques were "what was common in image recognition before the field became silly".