Core dumps are snapshots of a computer's memory stored onto disk when a program has crashed.
They are only of interest to a few programmers, and the average user has no use or need to save them. Since they take up several megabytes of disk space, you should turn off the option to have them generated. Otherwise, you will run out of disk space very quickly. This won't prevent your program from crashing but it will keep the system from filling your directories with core dumps.