First, the Algorand blockchain overcomes one significant problem that has been observed with any chain that becomes popular, a hard fork.
But, this is more of a feature than a problem.
The Algorand blockchain does not fork. Each new block is separately agreed upon and is guaranteed to remain on the Algorand chain forever.
I still wait to find out
how.
The Algorand consensus is not a drawn-out process. The fact that more and more blocks are attached to a given block B does not make it more and more probable that consensus on B has been reached.
So, when and how is consensus reached for sure?
Algorand separately reaches agreement on a new block. When this is done, it reaches agreement on the next block. And so on.
And yet, it's happening in every chain. Consensus happens separately, not simultaneously.
Thus, its users can immediately rely on the transactions as soon as they appear in a new block without having to wait for the block to become sufficiently deep in the chain.
Which brings me to
how again.
So instead of haggling with clients over an unconfirmed funds transfer (as may be the case with Bitcoin), a merchant accepting tokens that are underpinned by the Algorand blockchain is assured of the finality of the transfer
Algorand cures cancer.