When you drive, you pull down your visors to block the glare, or the blinding light from the sun. The "rocket's red glare" from the national anthem is the bright light you'd see as a rocket shoots through the sky.
Imagine the twinge of pain you get when you suddenly see the glare of a strong flash of bright light. Now imagine this light coming from an angry person's eyes towards you. This angry look is called a glare. If someone glares at you, be careful you don't get attacked! Glare can also mean the spotlight of public attention.