The whole concept of interest makes only sense if you have an inflationary currency. Bitcoin has a fixed maximum monetary supply. So it's wrong to expect interest, unless you assume that fractional reserve banking (essentially fraud) is taking place.
Therefore I advise caution when someone offers interest on Bitcoin deposits without offering a plausible explanation. Why do these exchanges offer interest? Why do they need more deposits?
Apart from reasons posted by others previously, I think another sound reason is that if the company behind these websites are big and have enough money to burn, they might just want to gain more attraction and users. This is like what many B2C, SNS and IM service providers did when they were in early stages. You might once asked yourself, why are they selling at such a low price, not even covering manufacturing cost?
Loyal users are the most valuable asset to any website/company. When Internet started, the number of clicks is what every website craved for. It is still true now. More loyal users means more trust, reputation, traffic, and eventually more money.
Bitcoin in China is new. But the competition here is fierce.
An early and strong start means huge advantage. Just plain old Matthew Effect.
Take Jua.com for example, the company that owns Jua.com has ChBTC.com (ChinaBTC Exchange), BW.com (cloud mining) and 8R.com (P2P lending based on BTC mortgage) behind it. BTW, I think those domain names alone cost a fortune. JUA users are more likely to use these services over others just because of trust and convenience.
Yes, giving away BTC as interest is a loss of money in the short term. But in the long run, it is hard to say.
If Bitcoin turns out to be a business of decades or even hundreds, this move of offering interest is a brilliant strategy to boost user number and gain reputation, as long as the company behind it is not just scam. This is the homework you should do.
Consider Youtube's counterpart in China Youku.com, Twitter' s counterpart weibo.com, and Amazon's counterpart JD.com. These are already very big brands in China for years, and they are still burning VC money and struggle to seize users and the market. I don't think currently there remains much opportunity for new starters to build anything like Youku / Weibo / JD in China and succeed. Admittedly it is still possible, but it's extremely unlikely to happen.
Additionally, more coins deposited means less coins dumped into exchanges and shorting leverage, which will contribute positively to btc price. Believers and HODLers will surely benefit from this.
So personally I think this way of gaining new users by offering interest is both understandable and justifiable.