If you will have a look in to reestablishment request message you will these IE's sent as reestablishment identity.
ReestabUE-Identity ::= SEQUENCE {
c-RNTI C-RNTI,
physCellId PhysCellId,
shortMAC-I ShortMAC-I
}
Importance of PCI
PCI is the previous cell PCI, before sending reestablishment with which cell it was previously connected with. So using this IE you can know with which cell UE was connected previously. So he can check the PCi info in his neighbor list and can take some intelligence decision.
Importance of CRNTI
C-RNTI also helps in the same way, let me tell you a scenario Suppose UE side RLF happened due to bad channel condition but eNodeB will mantain context of UE for some time, with in that time suppose that UE sends Reestablishment request to same cell then PCI + CRNTI will give unique identification and you can get the UE context in the same cell as before RLF UE was connected with this cell only.
Importance of MAC-I
As UE was connected with some cell previously so as part of security both UE and eNodeB security is activated, as due to RLF Ue lost his resource of SRB1 and SRB2 , so to send Reestablishment request UE have to use SRB0 only, But we know that SRB0 imposes no security , so as part of verification UE sends MAC-I of previous security context so that eNodeB can verify it.
Hope it helps.