Logstash is a tool for managing logs that allows users to collect logs from various sources, parse them, and output the data to multiple destinations. It provides inputs to collect logs from different systems, filters to parse and transform the log data, and outputs to send the data to places like Elasticsearch, Graphite, or other applications. The document provides examples of using Logstash to collect Apache logs, parse them using Grok filters, and output the results to Elasticsearch for searching and Graphite via StatsD for metrics.