Bitcoin Improvement Proposal 37 (BIP37), introduced by Mike Hearn and Matt Corallo, is a significant proposal that introduced "Bloom filters" to the Bitcoin protocol. This allowed for more privacy and efficiency in how lightweight nodes, often referred to as Simplified Payment Verification (SPV) clients, handle transaction data.

Prior to BIP37, if you were running an SPV client and wanted to know about transactions related to your wallet, you would have to download every single transaction from every block and filter them locally. This process was inefficient and used up unnecessary bandwidth.

BIP37 introduced a new method, where SPV clients only download a subset of transactions using Bloom filters. A Bloom filter is a data structure that's used to test whether an element is a member of a set. It's space-efficient and allows for a quick membership test.

In the context of Bitcoin, SPV clients set up a Bloom filter for their wallet addresses and send it to the full nodes. The full nodes then only send transactions to the SPV clients that pass the Bloom filter, i.e., are likely to be relevant to the client's wallet. This way, SPV clients don't have to download every transaction from every block, saving bandwidth and making SPV clients more efficient.

However, it's important to note that BIP37 does have some drawbacks. One of the main issues is privacy, as Bloom filters can leak information about the addresses in your wallet. Also, the use of Bloom filters puts additional computational burden on the full nodes in the network. In the years since BIP37 was implemented, alternative methods for SPV clients to efficiently manage transaction data while maintaining privacy have been proposed and developed.