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Curse of Dimensionality:

Assume you met a random individual at a seminar and later discovered he is a an alumni of your high school. Speaking with him/her further revealed that he/she attended a different school for Undergrad and Grad, and that his hobbies are diverse. Now that he works for a different firm, the first feature, that he went to the same school as you, may lead you to believe that he is your type (or a neighbor). Knowing more about someone may not help us feel like he's close to us.

The same thing will happen if we collect a large number of features with small data points, which will cause a dimensionality problem. Data in high-dimensional spaces are placed sparsely and not as close as possible. As a result, the accuracy of our model and its hypothesis cannot be as large at smaller dimensions. Also, with fewer data points and more features in a dataset, it is hard to create algorithms in higher dimensions with high confidence levels.