QoS is short for Quality of Service. For data networking, it refers to a set of properties that denote expectations for transport. It essentially covers network resource management. QoS can define levels for throughput, latency, jitter, etc. For example, multimedia streaming & voice applications are more sensitive to latency than data transfer applications. QoS is sometimes used to ensure that the right kind of network resources are present to provide good service for these applications.
In this case, however, QoS refers to controlling bandwidth usage levels. The "route-based" of route-based QoS involves setting QoS classes based on the destination of outbound network traffic.