The Segwit2x idea was first introduced by Rootstock’s Chief Scientist, Sergio Demian Lerner. Since then many miners and businesses within the bitcoin industry signed a pact during the Consensus conference in New York last month. The code itself is being worked on by a Segwit2x working group with Bitcoin developer Jeff Garzik leading the way. Since the alpha code has been launched mining pools are now signaling their support for the protocol implementation.
A recent Reddit public service announcement (PSA) that details how Segwit2x will actually work gives a great explanation of the entire process. Essentially if enough hashrate continues to support Segwit2x and reaches 80 percent over a 336 block signaling period that will lock in Segregated Witness. The protocol will then activate after another 336 blocks later for those running Segwit2x implementations. The Reddit thread also explains how the following hard fork (HF) after Segwit will be implemented on the main network.
If you keep your bitcoins on an exchange you are essentially at the mercy of what the exchange decides to do. Depending on how they upgrade their nodes, if they upgrade to begin with, it could seriously mess with your holdings. I highly suggest moving them to a trusted desktop or mobile wallet, such as Electrum, Mycelium, or breadwallet. I personally used Electrum and it is very nice and user friendly.
source: https://news.bitcoin.com/70-percent-bitcoin-hashrate-signaling-segwit2x/?utm_source=OneSignal%20Push&utm_medium=notification&utm_campaign=Push%20Notifications
https://www.reddit.com/r/btc/comments/6i16gl/psa_how_segwit2x_actually_works/
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