If the star is checked in a normal game there will be a big star, much closer thanthe other stars in the game. The star has a powerful gravitational pull. The danger from the stars heat is minimal to a star ship with shields, but it can take its toll on the ship if you stay in there for too long. Ships may be safe, but any torpedo that gets too close to the star will be destroyed.
Other than its gravitational pull, and it's heat, the other problem the star can cause is that any cloaked ship inside will show up on short range sensors.