Consistent hashing answers a question naive hashing gets wrong: what happens to cached keys when the node count changes? Modulo hashing remaps everything — a cache becomes a sieve. Consistent hashing remaps only the neighborhood of the change: adding a node moves the keys between it and its predecessor; removing one moves only its own keys onward.
Ownership is a walk, not a lookup: hash the key, step clockwise, take the first node. The ring's geometry does all the bookkeeping. Virtual nodes are the refinement that makes the geometry fair — with plain hashing, a few nodes means lumpy arcs and hot nodes; with 100–200 vnodes per physical node, ownership smooths out and per-node weights become expressible. That is why memcached layers, CDNs, and partitioning schemes all use the ring: membership changes cost O(1/N) of the keyspace in moves, and lookups stay a single hash and a walk.