The committed information rate (CIR) is the rate at which the network supports data transfer under normal operations, which is expressed as bits per second.
You have a contract with your carrier, who has committed to providing a given throughput, here called the committed information rate. You configure this value that the carrier provides per virtual circuit.

If you under-submit it doesn’t matter.
If you over-submit (called "bursting over your CIR"), excess frames may be discarded if the network gets congested.
When you’re renting Frame Relay lines, you need to discuss CIR figures with the Telco to ensure that the line can cope with the amount of traffic you intend to throw at it.

Congestion occurs when more data is attempting to cross the network than it can handle. When this is detected a congestion bit is added to a frame header to tell the sending FRAD it ought to slow down. It will then keep frames in its buffers until it stops receiving congestion bits.
If buffer space fills up, or there is none, then frames are discarded.
The network knows the CIR for a sender and discards frames that have had a Discard-Enable (DE) bit set in their header meaning that they represent a frame in excess of the sender’s CIR.
Some FRADs can set the DE bit to signal that the frame is low priority. Thus senders can divide messages into normal and low priority groups.

When configuring the CIR, consider the following:

CIR of 0

You can contract with a carrier for a CIR of 0, which yields best-effort service at low cost.
The carrier transmits data, but does not commit to providing any specified throughput.