Novice Question. What is SegWit? Why is it a big deal
Segregated witness is a method to fix transaction malleability. Malleability makes chains of transactions unsafe.
Imagine you had a chain of transactions that weren't submitted to the blockchain.
A spends from B and B spends from C
With transaction malleability, they can be changed after you submit them. Anyone who gets a transaction can modify it to make a different version. This means that as your transaction propagates over the network, some nodes could modify it before sending it onwards.
They can't change where the money is sent, but they can alter a valid signature into another valid signature.
Transactions refer to each other using txids. B would refer to C using C's txid (transaction id).
When you submit C, if it is modified by someone before it makes it to the miner, then it will have a different txid (even a tiny change alters the txid).
C' (modified C) could get accepted by the block chain if that miner gets the next block.
This means that B and A are now worthless. B spends from C, not from C', so it won't be accepted, even though it has a valid signature.
The way to fix this problem is to ignore signatures when referring to other transactions.
C and C' are identical, except for signatures. The unsigned txid is identical for both and can't be changed without invalidating the signature. If transactions referred to each other using the unsigned txids, then the malleability problem would go away.
This is a hard forking change, so was resisted by those who have object to hard forks on principal.
An alternative is to just remove all the signatures from the transactions. If transactions have no signatures, then inherently, the unsigned txid is the same as the normal txid.
Obviously, if people didn't have to sign their transactions, then the security of the whole system would fail.
Segregated witness was born. It has two parts. First, all signatures are remove from the (segwit) transactions and second, the signatures (witnesses) are all placed in a separate (segregated) data structure.
Note: the signatures are still checked with segregated witness. That is part of the point.
This is a soft fork and so was promoted by those who want to avoid unnecessary hard forks.
Fixing malleability is a reasonable goal. The objection was mostly that it would have been better to simply fix it with a hard fork.
The easiest change would have been to allow transactions to refer to the previous transactions by either the signed or unsigned txid. This would have required an extra database key for the unsigned tx though, so it wouldn't have been free.
Note2:
Segregated witness transactions actually include both the normal (legacy) transaction and the witness data as a expanded transaction.
These combined transactions are placed in the block as a single unit. These transactions have to be split apart and the witness goes into one merkle tree and the legacy transaction is used for the main merkle root.