A Bloom filter is a probabilistic data structure that can be used to answer a simple question, is the given element a member of a set? Now, this question can be answered via other means, such as hash table or binary search trees. But the thing about Bloom filters is that they are incredibly space-efficient when the number of potential elements in the set is large.
The filters allow false positives with a defined error rate - it gives the "yes" or "no" answer based on the content and you, the developer, decide if that answer falls within a rate that's okay for you and your app. The filters also take the same amount of time to look up items no matter how many are in the set.
He includes an example of the extension in use - defining the number of elements, the false positive allowance and adding/searching data and how the responses would come back from the checks.