I'm having trouble parsing the examples given in this thread; the above sounds like what I more-less understood from them.
So e.g. during the housing bubble, some companies were cash flow negative (i.e. losing money on their day-to-day business), but they recorded a profit for the quarter because the buildings they owned were worth more at the end of it than they had been at the start.
A business might have customers on a monthly plan, paying $2000 over their entire lifetime. If it costs $1000 in sales and set-up expenses to get a customer, they are profitable. But the expenses have to be paid up front, whereas the income will trickle in over a long period.
This means that even profitable companies might need to take loans or raise financing if they need to pay for expenses now, but the income from those sales arrives in months or years down the line. A cash-flow positive company doesn't have the risk of running out of money while waiting for the profits to come in.
Ideally, profit abstracts away all the messy details of cash flow. If you buy a new robot, that's not a loss, that's an investment, so your profit shouldn't change (until the robot starts depreciating). So profit (not cashflow) is a better metric. On the other hand, you don't know that the robot will really be useful, so maybe cashflow is better.
So for example, if you look at HP's write down, they were operationally cash flow positive for the quarter but are 'writing off' 8+ billion dollars. So they "lost" over $8B this quarter. Aka not profitable during the quarter.
So the milestones you look for as a company are that you are cash flow positive for the day (all of todays costs covered by revenue), cash flow positive for the quarter (net increase in cash on and over the quarter) and cash flow positive for the year (net cash increase for the year), and finally profitable (total income exceeded all costs, both tangible and intangible (like depreciation)).