What was segregated
BIP 141 defines a witness for each input. txid excludes witness, whereas wtxid includes it. A commitment in the coinbase binds the block to its witness data, which upgraded full nodes download and verify.
Why txid could change
Legacy signature or scriptSig encodings could sometimes be altered without redirecting funds, changing txid and breaking dependent unconfirmed transactions. For SegWit inputs, third-party witness changes do not alter txid.
Weight and compatibility
Block weight counts base bytes more heavily than witness bytes and is capped at four million units. Old nodes could accept the new witness programs under their looser rules, while upgraded nodes enforced the added conditions, enabling a soft-fork deployment.
More than capacity
BIP 143's SegWit v0 digest commits to the spent amount and avoids problematic repeated hashing. Versioned witness programs also supplied an upgrade path later used by Taproot.