What does "busier than a one-armed paperhanger" mean — and why is it funny?

informal, humorous

Meaning

Extremely busy; frantically occupied.

Where it comes from

An old American comic comparison. Hanging wallpaper is awkward, two-handed work, so doing it with a single arm would be a frantic struggle.

Why it is funny

The humor is the very specific, very doomed scene it conjures. You picture one person wrestling a long, sticky, curling sheet of wallpaper with a single arm — and instantly understand exactly how busy that is.

Used in a sentence

"During the holiday rush she was busier than a one-armed paperhanger."