what exactly does partially solved share mean?
you either find a winning-hash (equally to solve a block at difficulty 1) and get a share, or you don't.
what kind of partially work is there to take into account?
It takes time to get a share, partially means crunching numbers and not getting it before a block is found. That work is discarded and not taken into account.
There's no such thing as a partially completed share... If you're mining at 10 khash/s you're basically playing lottery 10,000 times per second.
That's true mining solo, coop mining you get paid proportionally to your shares.