Bloom Filter
A compact probabilistic structure that answers "is this key definitely absent, or possibly present?" — no false negatives, tunable false positives.
A few bits per element replaces holding the keys themselves, which is what makes it useful at scale. The asymmetry is the point: a negative answer is certain, so you can skip an expensive lookup entirely; a positive answer only means "check properly".
Where it shows up architecturally: LSM-tree storage engines put one in front of each on-disk table so a read can skip files that certainly do not contain the key, which is most of them. Caches use one to avoid a database round trip for keys that do not exist (cache penetration). Distributed systems use one to avoid shipping data the other side already has.
The parameters are size and hash count, which together set the false-positive rate; the classic limitation is that standard Bloom filters do not support deletion, for which counting or cuckoo variants exist.