Meaning /origin

half - pregnant
answer to a maiden's prayer

Meanings at least.

Half-pregnant. An impossible state to be in, because (obviously) it's a black or white deal, all or nothing. Often used to refer to someone who's trying to sit on the fence when it's impossible to do so - "you can't be half-pregnant, you know."

There is also the similar sounding "partially pregnant" which refers to the process of getting someone hooked on something: e.g. giving away a useful piece of software for free then, when people find it indispensible, insist they start paying for it. I first heard the term from an ex-IBMer.