Stars are basically suns (just like our own Sun) and are just as bright, if not a lot lot brighter.
However they are very, very far away, which means it takes a while for the starlight to reach us and when it does it has to pass through our very thick atmosphere so that we can actually see them.
When we see them, they appear to twinkle because of all the light rays are hitting off all the stuff in the atmosphere and they look really faint and they twinkle.
The stars which appear to not twinkle are actually things like satellites, the International Space Station and planets in our own solar system. These are a lot closer to us and therefore a lot brighter in the sky which means that we don’t quite see the twinkling quite as much.