When economic agents form their inflation expectations on the basis that the future will be like the immediate past i.e. if the inflation rate was 2% last year it is likely to be close to 2% next year.
Below is a graphical representation of how adaptive expectations affect the economy. In this instance there is a positive aggregate demand shock that creates excess demand and introduces inflationary pressures into the economy. If workers in the economy hold adaptive expectations, they will expect that inflation rate to continue for the following years and therefore will demand higher wages to prevent a future fall in real income. The higher wages then push up production costs for firms and ultimately that forces producers to curb production, resulting in the inward shift of the SRAS curve.
The key concept to grasp is that adaptive expectations will mean you get a classic progression from A to B to C over a period of time. However, if agents possess rational expectations the change in prices will be anticipated and there will be a more immediate move from A to C without the emergence of a positive output gap.