It's obvious if you view a proposition as a subset of all values in the proposition domain for which the proposition is true.
For example, a proposition "this umbrella is red" selects only red umbrellas form the set of all umbrellas that exist in the world.
A proposition "I own only red umbrellas" can be viewed as implication -
P is "I own this umbrella",
Q is "this umbrella is red", and it can be interpreted as "the set of umbrellas that I own is a subset of red umbrellas", that is, implication corresponds to "being a subset" relation in the set interpretation (similarly, conjunction corresponds to set intersection and disjunction corresponds to set union).
False proposition corresponds to an empty set - there are no values in the proposition domain for which it's true. From set theory axioms we know that empty set must be a subset of any set. This immediately gives you
"P implies Q" is true when P is false
It's essentially a formality, but a convenient one - for example if you don't own any umbrellas at all you can safely say "I own only umbrellas hand-made by unicorns from rainbows" and it's assumed to be true because it can't be disproved.