Triple Entry Accounting often refers to the ledger technology provided by blockchain.
Usually, when dealing with typical accounting ledgers, there are two categories: debits and credits. This is where we see double entry accounting come from. Under the rules here, one must have both, ie for each debit, there must be an associated credit.
It must always balance out.
Triple Entry Accounting adds the blockchain as a third option. While both debits and credits exist, the fact that it is all written to the decentralized ledger adds the third category. The latter cannot be changed once validated and lock on chain. Certain networks like Hive are now adding one block irreversibility where the third entry is settled in under 2 seconds.
Many term this an immutable ledger. All transactions are locked in.