The step-size parameter in an error-driven update: how far the estimate moves toward each new target.
Decaying reproduces the sample average, all samples weighted equally.
A constant gives a recency-weighted average: new and changing information stays relevant, old information decays (see). For non-stationary problems this is what you want.
It doesn’t really matter whether the step size is theoretically convergent: such schedules take ages to converge or considerable tuning effort to find a good/quick one. In practice, fixed step size is very common.