Each node of the Linked List has a very long string. And we repeatedly need to search this Linked List. Hence, at each node, there's possibly a very long comparison to make.
If there are n nodes, and length of each string is p, searching complexity would be $O(np)$ for a single search. For multiple searches, this would take a lot of time.
What we can do is calculate hash value of the input string, and all the strings in the nodes. By this method, only when the hash value matches, should we proceed and check string all the way.
With a wisely selected hash function, we can uniformly distribute hash values, and effectively reduce the search time from $O(np)$ to $O(n)$ for a single search.
To make things simple, assume number of nodes = size of string = number of searches to make = n. So, complexity = $O(n^3)$ for n searches
Precomputing hash values of all the nodes would reduce this problem to $O(1)$ comparison per node. So, complexity = $O(n^2)$ for n searches — a huge improvement.