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In many domains of science, measurements are done. If these measurements are drawn in a graph, they will be shown as simple unconnected points. Such data is called discrete. Handling and analysis of the data is easier, if it can be described using a continuous function. In order to do this, the data between two measurements needs to be "invented". This process is called interpolation. There are different ways to invent the data, such as simply drawing a straight line between to data points, or using polynomials. Interpolation assumes that the resulting curve will be "smooth". In many cases, the results of this interpolation are usable.
Interpolation tries to find the values between two known points of data, extrapolation is a similar process that tries to find data points at the edge or outside the currently defined points.