The two embraced on the street, oblivious to everyone around them.
Tips
history
From《史记·刺客列传》: Jing Ke and Gao Jianli would sing and weep together in the Yan marketplace 旁若无人 — utterly absorbed, as if no one else existed. Originally neutral, the idiom now leans negative.
usage
Modern use is mostly critical: rude, arrogant, or shameless behavior in public. The classical sense (deeply absorbed in something) survives mainly in literary writing.