We see light from stars that has passed through our atmosphere. Because of this, the atmosphere plays a big role in how we see the stars. Sometimes it causes the stars to twinkle, but clouds (which are difficult to see at night) may also temporarily obscure stars from our vision.
Yes, as Joseph said, it is really just an illusion. But stars do actually really die and then new stars are born, but these timescales are so huge that we do not observe much of this activity. We have observed some stars dying, and our latest telescopes are allowing us to see new star systems being born. Typical lifetimes of stars like our Sun are about 9 or 10 billion years. About 900 years ago a new star appeared in the sky that was so bright that it almost outshined the moon. It was a nearby star dying in a supernova event. If we point our telescopes to that region now we see the leftovers of the explosion as a big colourful cloud called a supernova remnant.
Stars can certainly appear and disappear, this is part of their life cycle.
But you say disappear and reappear, hmm? Perhaps you are thinking about a pulsar. Pulsars are rotating neutron stars that emit electromagnetic radiation (so we can detect them) that can only be seen when the beam points towards Earth. In this sense, they blink, or disappear and reappear.
There is also an Irish connection here. Dame Jocelyn Bell Burnell, born in Belfast, discovered the first Pulsar. She missed out an a deserved Nobel prize largely because she was female(!) PhD student.