In k-Nearest Neighbor classification, the training dataset is used to classify each member of a "target" dataset. The structure of the data is that there is a classification (categorical) variable of interest ("buyer," or "non-buyer," for example), and a number of additional predictor variables (age, income, location...). Generally speaking, the algorithm is as follows:
Of course the computing time goes up as k goes up, but the advantage is that higher values of k provide smoothing that reduces vulnerability to noise in the training data. In practical applications, typically, k is in units or tens rather than in hundreds or thousands.