The most common usage of the period, in English grammar, is to denote the end of a thought that is neither a question nor an exclamation. To be a grammatically correct sentence, the thought must be able to stand alone.
Periods are also used to indicate abbreviations, including times, like 10 p.m., and date, like Fri., Oct. 30. They are also used in numbers to separate whole numbers from decimals, like $13.38, for example. Three consecutive periods are known as an ellipsis. Ellipses are used to indicate an incomplete thought and often require the reader to complete the rest of the thought for themselves.