あっての

Hello, I can't really figure out what does あっての mean. WWWJDIC lists it as (adj-f) which can exist solely due to the presence of; which doesn't actually make much sense.

The example sentences lists 「命あっての物種。」as "While there is life, there is hope." but it isn't really very useful in explaining the usage of あっての.

Basically I was wondering what does あっての mean ?

This was a old JLPT1 grammar point, it's more a grammar pattern than an individual word. AあってのB = A must exist, or else B cannot exist (B does not necessarily exist if A exists, but A is a necessary condition for B). Focus on the fact that A is necessary for B.

Example sentence courtesy of Google:
お客様あっての仕事ですから、お客様を第一に考えることは当然です。

Instead of ＡあってのＢ you can also see forms like BはＡあってのことです。
これは皆様のご支援があってのことです。