Public permissionless blockchains use a decentralized consensus algorithm that prevent single parties from blocking "unwanted" transactions. Anyone can send a transaction, no one can prevent this transaction from being recorded. If you take Bitcoin and its Proof-of-Work algorithm for example, there's no single mining pool that could prevent you from sending a specific transaction. Even if there's a mining pool that doesn't want your transaction to enter the blockchain any other miner can jump in and add the transaction instead.
Private permissioned blockchains are managed by a central entity that ensures that only "wanted" transactions are recorded. Only specific users can send a transaction, the central entity can deny this transaction. In this respect they are more like classical databases where only a limited set of users is allowed to make a new entry.
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