A continuous graph is a graph that describes a space containing smoothly connected numerical values. There are no values excluded in between individual points on this graph. Continuous graphs are sometimes conflated with continuous functions, which are smoothly connected plot lines or shapes.
A continuous graph or function can be described in opposition to a discrete graph or function. Discrete graphs contain only certain specific values. Values in between these points are completely excluded and do not exist on that graph. These excluded values are called discontinuities. If a function that contains discontinuities is plotted, the discontinuities resemble breaks or holes in the plot.