Instrumenting your Crystal application with OpenTelemetry and New Relic can help you find and fix errors and performance issues in your production systems. The process involves adding instrumentation to your code, configuring OpenTelemetry, and sending data to New Relic using the OTLP/HTTP protocol. With auto-instrumentation, you can collect data on how long it takes to calculate Fibonacci numbers in your application, as well as what numbers are being calculated, without manually adding spans like this in a production environment. The example code demonstrates how to instrument a simple Crystal service and send its traces to New Relic for visualization.