ClickHouse provides a powerful date and time function called `date_diff` that enables users to calculate the differences between two dates or timestamps. The function has various syntax options depending on the unit of measurement, such as days, hours, minutes, and seconds. Users can use this function to perform calculations like finding the number of days between two specific dates in a table, calculating customer retention by determining how long it's been since a customer's last order, or filtering data based on time intervals. Additionally, ClickHouse offers other date and time functions that can be explored for effective manipulation and analysis of date and time data types.