In Load Balancing, when user (user id/ machine id/ cookie) is used for the hash function and m servers exist, the user is redirected to h(u)%mth server (where u is the key). When the number of servers n changes, all the mappings (for all n keys) change, and all the cache and user activity data on the server is lost. This is the problem consistent hashing solves.
Consistent Hashing is a technique such that when a hash table is resized, only n/m keys need to be remapped on average where n is the number of keys and m is the number of slots.