In the USA and CAN, L1 (black wire, narrow prong) is 120Vac with respect to Neutral (white wire, wider prong). Green wire (round prong) is tied to grounding rod under your electrical panel. Neutral is also connected to the ground rod (in just one place, inside the panel).
It is ok to touch the white wire, or the green wire with impunity; not so much the black wire.
Your scope has a three wire cord, so its outside case is intrinsically grounded through the green wire in its power cord. You have a 120Vac-powered non-isolated project on your work bench. You are probing around with the scope probe to see voltages inside the project. Scope probe ground-clip has a direct path to the scope case, and back to earth through the green wire. Where do put the scope ground-clip? If you guess wrong, and select something with a path to L1 (black wire), instant flash as you vaporize the ground clip on the probe. Flash is big enough to burn you or flip molten metal into your eye.
Or with one hand you touch something in the project that has a path to L1 (black wire), and with your other hand touch the scope face. Scope face is grounded. Current path is from L1 in the exposed wiring on your bench project, through one arm, through your chest, across your heart, out the other arm, to the scope. Your wife gets to call the paramedics.
Either of these scenarios are effectively prevented by putting a low-leakage 1:1 120Vin/120Vout isolation transformer between the wall socket and your project.