Smoothing is a statistical technique that helps you to spot trends in noisy data, and especially to compare trends between two or more fluctuating time series. It's a useful visualization tool that I'm pleased to see cropping up more and more in statistical graphics on the Web -- it's now a staple in econometric charts and is heavily used in polling analysis. For example, here's smoothing used to combine data from various polls over time on Obama's job approval (from pollster.com).
The S language was, to the best of my knowledge, the first software that made statistical smoothing a core part of the graphics system: first with the lowess function and later with other more powerful alternatives. These days in R (S's successor), loess (local polynomrial regression fitting) is the usual go-to alternative for smoothing. With just a couple of lines of code, you can take a noisy time series in R and overlay a smooth trend line to guide the eye. Nathan Yau at FlowingData shows us how to take data like this:
FlowingData: How to: make a scatterplot with a smooth fitted line