Someone older than myself correct me if I'm wrong.
what exactly is the contents of this file?
The wallet.dat file contains all of the private keys to your addresses (which are needed for you to send funds to another address).
Is it safe to keep on a pc?
It's as safe as you're willing to make it; there are many posts about how to protect your wallet.
Should it be stored offline?
What should be stored offline, and what is ok to keep on a pc?
Personally, I keep "walking around money" on my computer and "BTC I'm not ready to spend yet" offline.