In Common Lisp, quoted objects are constant literal data. You should not modify this data, as the consequences are undefined. Possible consequences are: modification of shared data, attempt to modify read-only data, an error might be signalled, it might just work, ...
For lists:
'(1 2 3)
Above is a constant list, which will be constructed by the reader and evaluating to itself, because it is quoted. If it appears in Lisp code, a compiler will embed this data somehow in the FASL code.
(quote (1 2 3)) is another way to write it.
(list 1 2 3)
this is a call of the Common Lisp function LIST with three arguments 1, 2 and 3. When evaluated the result is a fresh new list (1 2 3).
Similar:
'(1 . 2) and (cons 1 2)
'#(1 2 3) and (vector 1 2 3)
One is the literal data and the other is a function call that constructs such a data structure.