Analysts study the curve to assess the likely course of the economy. A steep curve (i.e. the yield on longer-term bonds is considerably above shorter-term bonds) typically indicates a pick-up in economic activity. A steep curve is generally the result of an aggressive Fed pushing short-term rates lower. Today's curve is steep.
A flat or inverted curve typically presages a slowing economy. It generally follows an aggressive Fed-tightening move whereby short-term rates are driven higher. If we experience an inflationary episode in the coming years, this is probably what we'll see.
As a point of useful information, it is generally agreed that the Fed controls short-term rates by targeting the federal funds rate at its FOMC meeting; and longer-term rates reflect inflationary expectations.
In today's environment, the Fed seems to be trying (and succeeding somewhat) to influence longer-term rates by its so-called policy of "quantitative easing." This policy involves buying longer-term securities which pushes their prices higher and yields lower.
Although the Treasury yield curve is the most closely followed, there are others worth knowing about. One such is the TIPS curve which shows the yield on various maturity Treasury Inflation Protected bonds. This curve can be found at the Bloomberg site :

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