Methods to improve Time series forecast (including ARIMA, Holt's winter)

From the above pic in case of Moving Average what does rolling(60) mean here? Is it the last 60 days of the train data set? or, Why 60 is used please specify?
As far as I understand <train[‘Count’].rolling(60).mean().iloc[-1]> mean the last mean of train is used.
Also the len(y_hat_avg) is 61 so how can 60 window can be taken into account?

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