The mini-blockchain scheme is a variant of the Bitcoin protocol which aims to eliminate the need for storing a full blockchain and overcome the "blockchain bloat" problem. The mini-blockchain is essentially like any other Bitcoin-based blockchain except that old blocks can be pruned from the chain. The block headers are kept as a PoW record but all old transactions can be discarded.
Address balances are managed separately in a hash tree structure called the account tree which is essentially a self-contained balance sheet designed to keep track of all non-empty addresses. New blocks act upon the entries in the account tree to perform transactions and the master hash of the account tree is embedded into the block headers to ensure consistency and agreement between nodes.
Since a proof-of-work is required for each new block, the account tree is updated in relatively periodic intervals of time. Since the master hash of the account tree is embedded into the block headers, the mini-blockchain helps to protect the account tree from malicious changes. However if we're discarding old blocks the mini-blockchain is not secure unless we keep the block headers.
So to secure the whole system from attackers, we use a chain of interlocking proof-of-work solutions termed the proof chain. The proof chain is simply a chain of block headers which encapsulate all the energy expended by the network on a given chain. The chain of block headers feeds into the mini-blockchain and acts to secure it and the account tree against attackers, even without old transactions.
The mini-blockchain, the account tree, and the proof chain, form the 3 core components of the overall scheme and work together to create a highly secure and robust P2P transaction system very much like the Bitcoin system but with a much better level of scalability, bandwidth, and speed. By optimizing each core component to perform a certain function of the blockchain we achieve unparalleled compression with a high level of security.