I don't believe she knows the literal meaning until she travels to Braavos (presumably she learns from the crew of the ship that takes her there). From what I recall, Jaqen H'ghar merely tells her to repeat the phrase and give the coin to any Braavosii, but doesn't explain what the phrase means.
However, the phrase "Valar Morghulis" becomes a talisman of a sort to her. She uses the phrase, coupled with her "prayerprayer", as mantras to steel her resolve and help her through times where the old Arya might have been afraid.
The fact that she says the phrase when she witnesses death is only somewhat coincidental, but doesn't indicate she knows the literal translation of the phrase.