Hi,
The threshold in any given MOSFET will be somewhere between -1V and -3V. So if you buy a bag of 3 MOSFETs, one might have a threshold of -1.5V, one might be -2V, and the last might have a threshold of -2.5V. Just as an example.
Now, for any given P-channel MOSFET, (loosely speaking) the MOSFET is ON if Vgs is less than the threshold for that particular MOSFET. So if a particular MOSFET has a threshold of -1.5V, then it'll be on for any Vgs < -1.5V, and off for any Vgs > -1.5V.
In reality, the turn-on/turn-off is not a hard switch like a light switch as I've implied above, the threshold is actually defined as the Vgs where Id has a mere 250 microamps leaking through, so it's just the threshold where it starts to turn on.
So that's the explanation of what the datasheet means. In terms of designing a circuit to use these MOSFETs, you want your Vgs to significantly > -1V in order for the MOSFET to be off, and very significantly < -3V if you want it to turn on (because remember, some of the MOSFETs might have a threshold near -3V, which means that even with Vgs at -3V, those will only allow 250 microamps through, which hardly qualifies as being "on" in almost any application.) It looks like you'd really want Vgs to be -4V or -5V or less for it to be really properly on, based on the graph.
EDIT: Also, whatever PDF viewer you are using is screwing up the PDF. The test conditions that you outlined are supposed to be "VDS = VGS, Id = -250 uA", but the micro simple has mangled the end into a not-equals sign with an A after it. You might want to find a way to fix that, reading datasheets is hard enough without your computer mangling the symbology.