This image above shows the recent demise of Comet Ison (courtesy of Ars Technica). The comet, which you can see on the bottom-left gets very close to the Sun and comes around the back-side, but much smaller than before.
The sun is a giant nuclear-fusion reactor, and although the comet was 1.2 million kilometers away, the temperature was already 2,700°C and the sun’s gravity would rip the comet apart. Since the comet (suisei 彗星 in Japanese) was so big, people thought it might survive, but it didn’t. Someone wrote an amusing eulogy for Comet Ison which is interesting to read.
All comets are leftover material from when the Solar System was created, so they are about 4.5 billion years old. Usually they sit deep in space in the Oort Cloud, until something causes them to fall inward toward the Sun. Some comets only appear once and never return, while others come regularly. But all of them are ancient rocks and snowballs, and most will probably never come to our Solar System.
It’s amazing what goes on in this Universe of ours.