The "feefilter" p2p message is used to inform other nodes of your mempool min fee which is the feerate that any new transaction must meet to be accepted to your mempool. This will allow them to filter invs to you according to this feerate.
As suggested by Greg Maxwell-- unit test to make sure a block
with a double-spend in it doesn't pass validation if half of
the double-spend is already in the memory pool (so full-blown
transaction validation is skipped) when the block is received.
Pieter Wuille