Axiom's live streaming feature allows users to easily view, filter, and extract logs from various data sources in real time, enhancing the ability to diagnose and evaluate system performance. By creating datasets and ingest tokens, users can import events into Axiom using APIs, data shippers, or Elasticsearch Bulk API. The tutorial guides users through setting up filters and exploring operators to refine log searches, enabling the extraction of specific data insights based on field criteria. Users can manipulate the stream's display settings, such as text size and field visibility, and save their searches for future use. The stream feature offers both a live mode, which continuously updates with new events, and a time range mode for viewing specific intervals, providing flexibility in monitoring and analyzing data.