To what extent is it acceptable to copy definitions from reference materials?
Is this acceptable if I include a portion of introductory matter of a source text if the source material is referenced? 


There are two issues here.  One is whether you can be accused of plagiarism.  That's simple: you're safe if you cite the source and clearly indicate what was copied with quotation marks or a block quote, but you could be in trouble if you don't make it clear what was copied, even if you cite the source.  (Occasionally you can avoid quotation marks by saying something like "The following definition is taken verbatim from reference [3]:", but it's risky to try that with longer quotations.)  If you are not copying any text, then you still need to cite the source but you don't have to worry about plagiarism.

There's also the issue of whether extensive quotations are acceptable to your advisor, regardless of whether they are plagiarism.  Even if you cite appropriately and use quotation marks, your advisor might think you are quoting too much and ask you to rewrite it in your own words.  (But this isn't a matter of academic honesty, just of what constitutes a good thesis.  Relying on lots of lengthy quotations is honest but lazy.)

Students sometimes worry about how much text is appropriate to copy from a definition without quotation marks.  This is a little tricky, since there are certain standard phrases that get used repeatedly.  For example, the definition of a group in mathematics might start "A group is a set equipped with a binary operation".  I just wrote that myself, but a web search reveals that half a dozen people have used exactly the same wording (because it's a pretty standard way to express things).  If you read a definition that starts this way and later use this phrasing when defining a group, that's not a problem.  However, you shouldn't be copying elaborate definitions verbatim without attribution.

In particular, if a standard phrase sticks in your head and gets repeated when you write the definition, that's fine.  One test is whether you need to copy from a book.  If you can write a clear, correct definition without copying or looking at any materials while writing it, then you should do so (and you won't have to worry about plagiarism).  If you can't write a clear, correct definition without copying from a reference book, then you need to cite the book and indicate that the definition is copied (since this is clearly a complicated or subtle enough definition that formulating it well deserves credit).