What does it mean for amplifiers to be stable only down to N gain, where N > unity?
To expand on my comment, they are talking about closed loop gain.

If an op-amp is not unity gain stable, it has to be stable under some conditions, or what's the use of it? 

So, if they say the op-amp is "gain-of-3 stable", they're telling you, this op-amp is not unity gain stable, and the minimum gain where it is stable is 3.