What's the meaning of "Pāli" and its relevance in regard of the Buddha's Dhamma?
According to British philologist and Professor Emeritus of Indian Studies at Cambridge University, Kenneth Roy Norman, Pali was mistakenly made to be the name of the language of the Canon. He explains how, below. He also links it to the Canon.

From "The Pāḷi Language and the Theravādin Tradition" (1983) by Kenneth Roy Norman:


  The dialect  of Middle Indo-Aryan which is found in the texts of the
  Theravadin  Buddhists and usually called "Pali" by European scholars
  is nowhere so called in the Theravadin canon. The word pāli is found
  in the chronicles and the  commentaries upon the canon, but there it
  has the meaning "canon" and is used in the sense of a canonical text
  or phrase as opposed to the commentary (aṭṭhakathā)  upon it. This
  usage is made  clear by the  fact that  the  word pāli sometimes
  alternates with tanti.
  
  It would seem that the name "Pali" is based upon a misunderstanding of
  the compound pāli-bhāsā "language of the canon", where the word
  pāli was taken to stand for the name of a particular bhāsā, 
  as a result of which the word was applied to the language of both canon and
  commentaries. There is evidence that this misunderstanding occurred
  several centuries ago.


According to Bhikkhu Bodhi (from here - taken from "In the Buddha's Words" (2005), Wisdom Publications, page 10):


  Scholars regard this language (Pali) as a hybrid showing features of
  several Prakrit dialects used around the third century BCE, subjected
  to a partial process of Sanskritization. While the language is not
  identical to what Buddha himself would have spoken, it belongs to the
  same broad language family as those he might have used and originates
  from the same conceptual matrix. This language thus reflects the
  thought-world that the Buddha inherited from the wider Indian culture
  into which he was born, so that its words capture the subtle nuances
  of that thought-world.