1. Table calculations allow you to perform calculations on the fly within Looker reports to add new columns or metrics without modifying the underlying data model. They use Looker expressions rather than LookML.
2. The document provides examples of using mathematical functions like sum and rand, string functions like contains, and date functions like diff_days in table calculations to calculate new metrics like percentages of users by gender, average items delivered per week, and time to delivery.
3. Tips are provided like avoiding sorting on reports with many rows, limiting result sets before aggregation, and hiding table calculations from visualizations.