We might merely wish to plot the data as a simple curve. Alternatively we might have a theory which tells us the form of the curve and gives a specific interpretation to the parameters of the curve. Let us start the discussion by setting up a few categories for the data. These categories are not mathematically precise criteria, but they clearly affect the way we will process the data. This isn't very fundamental, but it can make life a lot easier.
Mathematical expressions are often simpler with evenly spaced x-values.
Computed curves and some experimental curves may have little or no noise and we may expect the curve to pass through all points. With most experimental data this is not true. Obviously if we have 50 points over the peak we will have a lot of detail and we could afford to use averaging to cope with noise. Sometimes you collect your own data, write it into a notebook, and later transfer the data to a computer program. When this occurs, you are likely to have 5-50 data points and the points are often irregularly spaced.