What is an S-Curve?
The S-curve is cumulative cost (or work) plotted over time. It's S-shaped because projects spend slowly at first (planning, mobilization), fast in the middle (peak execution), and slowly again at the end (closeout). The baseline S-curve is the time-phased budget in picture form.
In earned value reporting you draw three of them — planned value, earned value, actual cost — and the gaps between the curves are your variances, visible at a glance.
Worked example
A refinery turnaround's baseline S-curve shows $2M spent by week 2, $18M by week 6, $24M by week 8. In week 5 the actual-cost curve tracks the plan but the earned-value curve sags 10% below — money is flowing on schedule, work isn't. The shape told the story before a single report was read aloud.