Bitfinex is a popular exchange because in terms of USD trading volume it has the most liquidity. It currently owns about a 10% share of the USD trading market.
Because of its confusing interface, it's probably only a good choice for traders who really know what they are doing.
Despite getting hacked and losing $70 million or more in customer funds, Bitfinex remains a popular option for serious traders. Still, the hack is scaring some people away.
Verification
One thing that has made Bitfinex popular is that if you only make a deposit with cryptocurrency no verification is required. If you want to deposit dollars or euro then you WILL have to verify your ID.
Fees
Bitfinex offers very low fees even for low volume buyers, at 0.1% per buy for market makers and 0.2% per buy for market takers.