Metric field represents the details of the host such as age, source, RTT,cwnd. Every metric is unique in itself as every ip address has a different metric so routing behaviour would be deiffernet fro every metric.
In the context of the routing table, the metric field signifies a numerical value assigned to each route, serving as an indicator of the route's preference. A lower metric implies a more favorable or efficient route. The Linux kernel utilizes these metrics to determine the optimal path for transmitting data to a specific destination.