I read this in a IRC exchange:
verifies your txns against a random node that you don't control. if for some reason that node went rogue, you might have accepted an invalid txn
What is a txn?
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It's short for "transaction". There is a list here of rules that individual transactions must follow:
Some reasons that a transaction could be invalid are:
-The person trying to spend bitcoin doesn't have that much bitcoin.
-The person trying to spend bitcoin already submitted another transaction trying to spend the same bitcoin.
-The person trying to spend bitcoin can't prove that they are the owner of the bitcoin.
In addition, the block as whole that the transaction is in must follow these rules: https://en.bitcoin.it/wiki/Protocol_rules#.22block.22_messages
"txn" is short for "transaction". The abbreviation "tx" is also often used.
For an explanation of what makes a transaction (in)valid, see the links at How to know if a transaction is valid?