The acronym seems to mean "move instantaneous rewards" (link), but I can't find any good ELI5 explanation on what that means, when would I require a MIR certificate, etc.
"MIR" is not a particularly good name, but I can explain the history.
It started out standing for "move ITN rewards", where "ITN" stands for the "incentivized test net". The idea of the ITN was a test network whose rewards would end up on the main network after the launch of the Shelley phase. The MIR certificates were originally designed for exactly the purpose of transferring Lovelace from the reserves on mainnet to the participants of the ITN (and requiring authorization using the existing governance mechanisms).
It eventually became clear that this mechanism would be useful for more purposes than just the ITN rewards, such as paying out Catalyst winners from the treasury. So the acronym was re-imagined to stand for "move instantaneous rewards", since they transfer funds at the next epoch boundary.
An ELI5 explanation of MIR certificates is: MIR certificates require the authorization of the existing Cardano governance mechanism, and they result in the transfer of Lovelace from the reserves or the treasury to a collection of stake credentials. (They can also move Lovelace between the reserves and the treasury.)
Not sure about the exact purpose of MIR (move instantaneous rewards) certificate but it seems to be a specific type of transaction to allow for 'transferring funds between reserves and the treasury'.
My guess would be for funding things like Catalyst projects.
This link will tell you what instantaneous rewards are.