On most blockchains like Bitcoin, network transactions are linked together. Essentially spending Bitcoin creates an output from a transaction and transforms it into an input of a new transaction. If a previous transaction is invalid, the new transaction that relies on the older one will become invalid. Which leads to the problem that all nodes must have a backlog of all the transactions that ever happened on the entire blockchain. Currently we are looking at about 170 Gigabytes worth of data and it only grows bigger.
With the MimbleWimble protocol there is no longer really such a thing as a transaction history per coin. Each coin does have a specific block in which it was first created. But from then on, its value simply becomes part of the combined Unspent Transaction Output (UTXO) set, which defines all outputs that store coins and could potentially be spent at any time.
With the integration of the MimbleWimble protocol, nodes no longer need to care about previous transactions. All they need to care about is that the specific outputs used are valid.
With even more clever math, nodes can establish the validity of outputs relatively easily. They just need the block headers of all blocks (a sort of index of blocks without all transaction data) and the aforementioned dummy output signatures: both relatively compact data-sets. All other transaction data — almost the entire blockchain — can be safely discarded.
The benefits are substantial, that's why MoneroV plans to integrate the MimbleWimble protocol so that the blockchain size will be bound to the number of users using MoneroV (not the number of transactions being made in the network).
This will significantly reduce both transaction costs and blockchain size, where other Blockchains necessarily would have to grow over time, the required MimbleWimble dataset does not, which would solve the scaling problem.
