I think it means you can treat the locked object as if you didn't cast the spell to keep it locked, ignoring any possible failures for attempting to open it and failing horribly.
Obviously, if it still has a regular lock, you'd have to bypass that as normal, though per RAW, the Arcane Lock's benefits still apply (i.e. it's now a DC 30 check instead of a DC 20), even if you cast the spell yourself (letting you pass it freely without affecting it).
An arcane lock spell cast upon a door, chest, or portal magically locks it. You can freely pass your own arcane lock without affecting it. If the locked object has a lock, the DC to open that lock increases by 10 while it remains attached to the object. If the object does not have a lock, this spell creates one that can only be opened with a DC 20 Disable Device skill check.What does "You can freely pass your own arcane lock without affecting it." even mean exactly? The only thing I can't think of multiple readings is that you can open and shut a door/chest/portal without a physical lock that cast Arcane Lock on without any keys needed. What does it mean for something with an existing lock?
You normally cast the spell on something of your property. An arcane lock cast by a character doesn't affect him, so can open or close the object the spell is attached to as if the spell wasn't there.
Let's say you cast arcane lock on two coffers. One simply has a lid, the other has a physical lock with a key.
a) You can open the chest with the lid just by raising the lid. Other creatures attempting to raise the lid will have to deal with a DC20 magical lock.
b) You can open the chest with the normal lock if you have the key (or by rolling against the DC of the lock if you lost the key). All other creatures will have to deal with the DC of the lock +10.