I'm pretty sure that "plausible" is used with its standard, non-technical meaning here, and refers to the mechanism by which your data is generated.
For example, if you have data on temperatures in your area and data on your electricity consumption, it's plausible that warmer temperatures will lead to more air-conditioning use and hence higher electricity use.
On the other hand, if you have data on the number of cookies sold in your area, I can't think of a plausible mechanism by which this would cause you to use more electricity in your home.
It may be that there is a plausible mechanism but you don't currently know enough to clearly see what it is. For example, you may see that various sea surface temperatures in the Pacific Ocean are correlated with drought conditions in Texas, but not know of the atmospheric mechanism that might underly this. Two hundred years ago, people may have been skeptical of any relationship over such a long distance, but today it's accepted and is plausible even without a deep understanding of meteorology. (To a meteorologist, it's extremely plausible.)
EDIT: In answer to your comment, "plausible" means "believable" or "reasonable", so a plausible explanation "makes sense". It's weaker than "proven", but stronger than "speculative".
If you do have a "plausible mechanism", it gives some amount of confidence that you can speak about causality. But it doesn't guarantee that you're right. If you do not have a plausible mechanism, then there is suspicion that you've merely found correlation and not causation. Not (currently) having a plausible mechanism doesn't guarantee that there can be none, as the caveat in your quote notes.
Also, just because someone says that XYZ is a "plausible mechanism" doesn't mean that knowledgeable people would agree. "Plausible" needs to be interpreted within a context. Plausible to the conspiracy theorist is not the same as plausible to a layman, which is not the same as plausible to a scholar in the field. (Which is where you may have gotten your connotation: someone saying something like, "it may be plausible that ..." meaning that there's a very slight, speculative possibility, but that's a verbal nuance.)