As is obvious from the title, The UE information procedure is used by E-UTRAN to request the UE to report information [1].
There are two different scenarios for the Network to send the UEInformationRequest message to the UE. One is to find out the number of RACH preambles it needed for the random access procedure and the other is to get the measurement information when a Radio Link Failure (RLF) occurred.
[2] also provides the following detail:
The network may poll for the UE report after a successful random access procedure (UEInformationRequest) and the UE responds with the number of preambles sent by MAC for the last successfully completed random access procedure and whether contention is detected by MAC for at least one of the transmitted preambles for the last successfully completed random access procedure (UEInformationResponse).
Source:
[1] 3GPP TS 36.331 V9.3.0: Radio Resource Control (RRC); Protocol specification - Section 5.6.5
[2] 3GPP TR 36.902 V9.2.0: Self-configuring and self-optimizing network (SON) use cases and solutions