There was a lot which went into them gaining such a high marketshare in a short period of time. Some of these include some exchanges being forced into following KYC info, which means they had to get information on people who were trading over a certain volume (something that Binance doesn't follow, as they give everyone a 2btc trading max per day for unverified) Their trading UI is pretty good, works flawlessly, this is something which is much better then other exchanges.
Last thing is the fact that their support is good, without this they'd be mediocre but their support really makes them something else. - Check here for more (
https://www.quora.com/How-has-Binance-managed-to-grow-so-much-volume-in-such-a-short-time)
