What it means
It means choosing the bit of good that still survived when a situation's gone a bit rubbish. You say it to cheer someone up or to stop a moan from taking over the room. It's that little mental pivot toward the upside, even if the upside is tiny.
Usage examples
"Look on the bright side, at least the rain means we can stay in and relax."
"We missed the train, but look on the bright side, now we have time for breakfast."
"Look on the bright side, the flight's delayed but at least the bar's open and we're in no rush."
"Lost the match but, look on the bright side, nobody pulled a hamstring and the curry after was unreal."
"Look on the bright side, your phone's smashed but now you've finally got an excuse to bin that tragic case."
Where it comes from
This isn't really slang with a traceable street origin so much as a long-standing everyday English idiom. It's built from the plain metaphor of turning your attention toward the bright part instead of the dark one, and it's been used in English for well over a century as a stock bit of encouragement.