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Period is a duration of time which is usually user determined. For example, a chart could be a minute chart, 30 minute chart, daily chart, etc. Each of those are considered to be periods.
Many different indicators use a Look-Back Period. This is the number of periods to be included in the indicator's calculation. Consider the example of a 21 Period Simple Moving Average, If you are looking at a daily chart, 1 day would be considered 1 period. The SMA would then calculate based on the previous 21 days (periods).