Short answers, pulled from the story.
SegWit, or Segregated Witness, is Bitcoin Improvement Proposal 141, a soft fork that changed bitcoin's transaction format by separating signature data from the rest of a transaction. It was designed to prevent transaction malleability, allow optional data transmission, and bypass protocol restrictions such as the block size limit without a hard fork.
SegWit activated on the 24th of August 2017, at block height 481,824. The activation window had opened on the 15th of November 2016 and required at least 95 percent of miners to signal readiness before the upgrade could switch on.
SegWit fixes malleability by separating the witness data, the unlocking signatures, from the rest of the transaction and serializing it apart from everything else. This keeps a transaction's identifier from changing even if someone tampers with its signature before confirmation.
A small group of mostly China-based bitcoin miners objected to bitcoin's SegWit plans and pushed forward their own proposal for a split. That split produced a separate cryptocurrency called Bitcoin Cash.
SegWit2x, also called SegWit2Mb or the New York Agreement, was a proposal announced in May 2017 by Digital Currency Group to activate SegWit and then a 2 megabyte block size increase within six months. Its developers canceled the planned hard fork on the 8th of November 2017, citing a lack of consensus.
In the first week of October, SegWit usage rose from 7 percent to 10 percent of network transactions. By February 2018, SegWit transactions exceeded 30 percent of the network.