The distance travelled over the time period represented by the area under the v-t graph between the end points.
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The area under an acceleration-time graph is equal to the object's velocity (not change in velocity).
A key can make it easier to interpret the data sets that each part of the graph represents, especially if there is no room in the graph area for labels.
It is not, if it is a graph of force against acceleration.
Displacement is the area under the v-t graph.
In statistics you can find the area under a curve to establish what to expect between two input numbers. If there is a lot of area under the curve the graph is tall and there is a higher probability of things occurring there than when the graph is low.