Peak information rate is a burstable rate set on routers and/or switches that allows throughput overhead. Related to Committed Information Rate which is a committed rate speed guaranteed/capped. For example, a CIR of 10 Mbit/s PIR of 12 Mbit/s allows you access to 10 Mbit/s minimum speed with burst/spike control that allows a throttle of an additional 2 Mbit/s. (This allows for data transmission to "settle" into a flow.)
Maximum Information Rate (MIR) in reference to Broadband Wireless refers to maximum bandwidth the Subscriber Unit will be delivered from the wireless access point in kbit/s.