The state is brought on by consuming drugs with visually brain-mangling psychedelic effects.
If said with a smile, one can assume the user is in a state of blissful confusion and wonder - but if said with a look of fear, one can assume the user is terrified and extremely paranoid.
* Dave is looking around at things with a look of extreme interest and happiness on his face.
<Pete> I'm tripping balls mate!
<Steve> How about you Pete?
* Pete is shuddering, wide-eyed, and looking incredibly sketched out.
<Pete> I'm tripping balls mate...
"DUDE, I'M TRIPPING BALLS!"
Probably originated from reference to 'tripping balls', as used by LSD users