What are your real-world applications of this versatile data structure?

They are useful for optimization in databases like sqlite and query engines like apache spark. Application developers can use them as concise representations of user data for filtering previously seen items.

The linked site gives a short introduction to bloom filters along with some links to further reading:

A Bloom filter is a data structure designed to tell you, rapidly and memory-efficiently, whether an element is present in a set.
The price paid for this efficiency is that a Bloom filter is a probabilistic data structure: it tells us that the element either definitely is not in the set or may be in the set.