Normally people don't focus their eyes on the sun; its always in the sky but noone usually has a reason to look at it so you never focus on it, and most know not to. During an eclipse thats exactly where you want to look and focus on, and focussing on it makes it even more dangerous (guessing due to time spent with same area of your retina receiving the focussed energy from it rather than moving around your view and unfocussed spot).
During totality (darkest part of 100% eclipse) your eyes start to adjust for the dark sky and open up, allowing even more light in; as sun comes out of totality it gets very very bright again quite quickly, and your eyes might not be ready for it - use protection as you see the diamond ring start to get bigger/brighter (or only look at the diamond ring on the way into totality for safest view, when its getting darker).
The same effect as totality is almost had by using eclipse glasses or other dark viewers that cover your head/eyes, and switching from that view back to unprotected view of the sun could be equally as dangerous for the same reason.
(I'm not an expert).