Data Science

Let's say we're an ice cream vendor tracking sales over time
Naturally, we would expect sales to increase in the middle of the year (i.e. summer) and sales to decrease at the end of the year (i.e. winter)
Therefore, ice cream sales clearly has a seasonal component

Seasonality is a characteristic of a time-series model in which the data experiences regular and predictable changes that recur ever time interval (e.g. one year, one week, etc.)
A cycle is somewhat similar, but it is not predictable
Specifically, seasonality refers to a repeating pattern every time period happening within a year
For example, if there is a yearly seasonal pattern, then a data point from this year and a data point from last year should be the same
Nearly every time-series model needs to be stationary, and one of the criteria for stationarity is that a time-series model can't contain a seasonal component
Therefore, we need to find a way to account for seasonality in our time-series models to satisfy the assumptiono of stationarity
We can do this by transforming our time series by calculating the differences (i.e. $z_{t} = s_{t+365} - s_{t}$ ), and thus using and ARIMA model

Seasonality refers to a predictable pattern over the course of some time period, whereas a cycle refers to a unpredictable pattern
Seasonality refers to more specific patterns, whereas cycles refer to more general patterns
For example, seasonal patterns would include any recurrent trend that happens exactly the same over time
On the other hand, cyclical patterns would include any general trend that happens over time, such as general increases over time (but not at exact moments in time)

References

Exponential Smoothing

SARIMA Model