Metrics are a way to measure things.
For instance in networks it is used to identify the cost of an operation. If you have a packet that needs to go from router A to router B. It can get their by either going trough router D or router C. Router A will calculate the cost, this is based on metrics. A router can calculate a metric by looking at what routing protocol is used by another router and its bandwidth. It will try to always use the router with the lowest metric.