Step 1: Spot the type of arrangement.
Eight different pearls are placed in a ring to make a necklace. This is a circular arrangement, not a straight line.
Step 2: Count circular arrangements first.
For $n$ distinct items in a circle, the count is $(n-1)!$. Here $n=8$, so we start with $(8-1)!=7!$.
Step 3: Work out 7 factorial.
$7!=7\times 6\times 5\times 4\times 3\times 2\times 1=5040$.
Step 4: Remember the flip.
A necklace can be turned over. So an arrangement and its mirror image look the same. That means we have counted each one twice.
Step 5: Divide by 2.
To remove the double counting, divide by $2$: $\frac{5040}{2}=2520$.
Step 6: State the answer.
The number of distinct necklaces is $2520$, which is option (C).
\[ \boxed{\,2520\,} \]