So if a lemonade stand has 3bn in cash it's done pretty well selling lemonade surely?
For a less ridiculous hypothetical, we know that BBRY has $3bn in cash right now. Supposing that it instead had $10bn in cash, its valuation would not be the same, it would be $7b higher. Its stock price (and equivalently its market capitalization) would reflect that, because the stock market is a place where people who disagree about the how to value the company go to make trades they believe are favorable. People who go to the public markets and act on the belief that ($10b in cash + a niche mobile phone business) should be valued at $5b would be rare. They would also be very wrong.
The current valuation of $5b implies that the niche phone business is worth $2b and the $3b in cash is worth $3b.
No, it is what the shareholder can, in principle, "take out" of the company, appropriately discounted. For a going concern, without excess cash, that is going to be, to a first approximation, something like discounted earnings.
> So if a lemonade stand has 3bn in cash it's done pretty well selling lemonade surely?
Not necessarily. When starting a business you need cash, even pre-revenue. Even if the cash were generated entirely from the business somehow the business endeavor may no longer be valuable. Maybe people don't like lemonade anymore. Maybe lemons have gone extinct. In those cases future earnings are zero.
If someone wanted to acquire the lemonade business what would they pay? Probably not $3bn because that would just be moving numbers around (there is no reason normally to buy cash). They would pay whatever they could get out of the lemonade business proper (assets, future earnings). The $3bn would be returned to the shareholders.