In a nutshell, it is a lightweight way to measure response times on a server such as a database, memcached, Apache, and so on. You can use this information for historical metrics, capacity planning, troubleshooting, and monitoring to name just a few.
The tcprstat tool itself is a means of gathering raw statistics, which are suitable for storing and manipulating with other programs and scripts. By default, tcprstat works just like vmstat: it runs once, prints out a line, and exits. You’ll probably want to tell it to run forever, and continue to print out more lines. Each line contains a timestamp and information about the response time of the requests within that time period. Here “response time” means, for a given TCP connection, the time elapsed from the last inbound packet until the first outbound packet. For many simple protocols such as HTTP and MySQL, this is the moral equivalent of a query’s response time.