The phrase suggests a high level of uncertainty, highlighting the unpredictable nature of an outcome. He's quite unpredictable—there's no saying what he'll do next.
Pro Tip 2/3
Not Literal
Used figuratively, it doesn't mean that literally no one can say, but rather that it's difficult to be certain. With the stock market so volatile, there's no saying if it's the right time to invest.
Pro Tip 3/3
No Assumption
The phrase warns against making assumptions about the future or unknown situations. There's no saying how long the power outage might last.