On the same site -- http://fakebuddhaquotes.com/better-than-a-thousand-hollow-words-is-one-word-that-brings-peace/ -- the author identifies the second quote as a slightly inaccurate or poetic translation of the 100th verse of the Dhammapada:
Sahassamapi ce vaca
ekam atthapadam seyyo
yam sutva upasammati.
- Better than a thousand words that are senseless and unconnected with the realization of Nibbana, is a single word of sense, if on hearing it one is calmed.
That too is not a literal translation into English -- http://www.tipitaka.net/tipitaka/dhp/index.php says they refer to the commentary if the literal meaning is vague or unintelligible or perplexing -- they added to the translation the phrase "unconnected with the realization of Nibbana" to clarify the difference between what they called senseless and sensible, i.e. between anatthapadasaṃhitā and atthapadam.
Here is maybe a more literal translation:
- Better than a thousand useless words is one useful word, hearing which one attains peace.
Note that's close to the version you quoted in the OP (it's so close that I don't see why what you quoted is listed as a "fake" quote, instead of being listed among the "real" quotes).
If you still don't understand it, I recommend the commentary/story which accompanies each verse (see here), and/or reading the whole chapter of the Dhammapada (see here).