A time-series is a list of dates, each date being a associated to a value (a number). Time-series are a structured way to represent data. Visually, it's a curve that evolves over time. For example, the daily sales of a product can be represented as a time-series.
In retail or manufacturing, time-series are important because they are the most canonical representations for the flow of goods either sold or produced. Representing business data as time-series typically help managers to visualize the activity of their business.
The graph here above represents, as two monthly aggregated time-series, the United States Web Search activity for the two search expressions cloud computing and asp.net mvc.
Forecasting time-series mean that we extend the historical values into the future where measurements are not available yet. Forecasting is typically performed to optimize areas such as inventory levels, production capacity or staffing levels.
There are two main structural variables that define a time-series forecast:
The period which represents the aggregation level. The most common periods are month, week and day in supply chain (for inventory optimization). Call centers typically rely on quarter-hour period (for staffing optimization).
The horizon which represents the the number of periods ahead that need to be forecasted. In supply chain, the horizon is typically equal or greater to the lead time.
Then, there are further subtleties related to the definition of the period itself, mostly because of calendar artifacts. For example, one can decide that the monthly aggregation starts on the Nth day of the month (instead of the 1st), but if N is greater than 28, it causes problems because not all months have more 28 days.