Sardinian is a language of its own, derived directly from Latin. So Italian and Sardinian can be considered "siblings". There are some terms in common, and my guess here is that since Sardinian is oral in nature (lack of writings during its history), many words have been lost or forgotten (for example, the word for rainbow is arcu 'e sole, but I doubt many know it).
What happened is that due to its isolation, since it's spoken in an island, the language evolved much less and slower compared to Italian.
For example, in Italian we had the loss of -um/-us endings replaced by -o, but as far as Sardinian is concerned, only the finals were dropped, leaving a lot of words with -u. This might not be a valid general rule since we say "Sardinian" for convenience, but the truth is that there are many varieties across the island, the closer a village/town is to yours, the closer the language. So someone from the north wouldn't understand what someone from the south speaks.
There are also differences in grammar. An example is the possessive which is usually put after the noun that it affects.
As I said, some terms are in common, but generally someone from other parts might not understand it, if any. For example:
it. Cosa stai dicendo?
en. What are you saying?
sar. Itte sese nande? (This should be read as "itte sernande")
Nande comes from "narrere" (to say), which is the same verb as "narrare" (to tell a story) in Italian.
Note that many things in this answer refer to the variety I speak, so others Sardinians might disagree about words or expressions. However the rest, which is what your question is about, is true for everyone.