I'm with [@André Carregal](https://photo.stackexchange.com/a/1374/5262): A big sensor, a lens f/2.0 or better and reasonable ISO handling.

For "how to tell", I suggest the [DxOMark low-light ISO tests](http://www.dxomark.com/index.php/Cameras/Camera-Sensor-Ratings/(type)/usecase_sports): Expand the _type_ filter and select _compact_ and _high-end compact_, and you get a list of cameras with their low-light ISO score.

Then check out test shots from the relevant models at [dpreview.com](http://www.dpreview.com/reviews/canons100/12), to see if the measured differences are actually visible in practice.

Here is an example screenshot from the dpreview widget, comparing image quality at ISO 1600 for compacts with different sensor sizes:

![DPReview ISO comparison][1]
(_The screenshot is compressed, see [dpreview](http://www.dpreview.com/reviews/canons100/12) for originals._)

* _Top right:_ Low-end compact, 1/2.3" sensor (sensor area 29 mm<sup>2</sup>) - Olympus mju 9010.
* _Top left:_ High-end compact, 1/1.7" sensor (41 mm<sup>2</sup>) - Canon PowerShot S100.
* _Bottom right:_ 1"/CX sensor (116 mm<sup>2</sup>) - Sony RX100. (This camera is not much larger than the Canon S100, and has an f/1.8-4.9 lens. At the time of writing probably the best low-light option that still fits in a pocket.)
* _Bottom left:_ APS-C sensor (373 mm<sup>2</sup>) - Fujifilm X100. 

Double the sensor area, and the sensor receives twice as much light during the exposure, all else equal. In theory, this gives a twice-as-large sensor a one stop advantage in low-light capability. Judging from test pictures as well as from the DxOMark measurements, the theory seems to hold up pretty well in practice. 

(_The main modifier for "bigger is better" is that sensor technology matters too: Sensor low-light performance improves at a rate of about one stop every five years, and a product may use a technology that's older/cheaper than the current state of the art. So "bigger is better" only holds when you compare "best of breed" for each sensor size at the same point in time. In the screenshot above, the low-end compact is probably not the best for its sensor size, but the others should be close to the top of their sensor class._) 
 
Of course, if you couple a more sensitive sensor with a slower lens (say f/2.8 instead of f/2.0), you sacrifice much of the low-light performance you just gained. So you want both: The most sensitive sensor with the fastest lens.

There's nothing to be gained in low-light performance from a camera with interchangeable lenses (versus a fixed lens camera with a similar sensor), other than the option of buying an f/1.4 lens (or even a manual focus f/0.95 lens for certain mounts). But then we're probably leaving the spirit of "point and shoot" behind.

  [1]: https://i.sstatic.net/RGm9l.png