Just to add to the other replies, there's another thing very different about a partial eclipse vs. when you looked at the sun as a kid. You were looking at a full sun, not a smidgen of a sun. There was so much light hitting your eyes that they stopped down naturally, giving you some protection.

And there was so much bright light that you really couldn't look at it for very long without involuntarily looking away or closing your eyes. But of course if you kept looking at the sun no matter how much it hurt, you would damage your eyes.

In a partial eclipse, most of the sun is covered, and there is a lot less light reaching your eyes. So they don't stop down as much as they would for a normal full sun.

However, that fraction of the sun that is visible is just as bright as before! With such an interesting sight to look at, you will be much more tempted to stare. And with your pupils wide open, there is even more sunlight hitting that small area of your retina than there would have been in normal conditions.

Now if you are fortunate enough to experience the total eclipse, that is another matter entirely. It is perfectly safe to look at the solar corona during totality, even with binoculars! The corona is only about as bright as a full moon. The sun itself is completely blocked by the moon.