Speaking from my own time at BMQ only, we were all required to do the swim test, which consisted of, If I remember correctly, you have to swim 50 meters continuously after jumping in feet first, while wearing coveralls. (Abandon Ship) The second portion of the test is having to tread water for two minutes, then swim twenty meters. However, it was not held against us if we failed it. Two guys on my course absolutely couldn't swim and passed just fine.
We were all navy too, so when civvies hear what I do and say: "I hope you're a good swimmer" I always respond: "Not a requirement in the navy."
EDIT: I did my BMQ in the naval reserves, so I can't say for sure it would be the same for you.
PO stands for performance objective, which is a test you are required to pass. Failing too many will result in being RTU'd - Returned to Unit(If you are doing BMQ as a summer course, I don't know how weekend BMQ courses work that)
Now that it's been mentioned, I cannot recall if those two individuals got PO failures for the swim test or not. They might have, but if that was the only thing they failed, they would have still passed.