Startup Disk Full: Core File
They are coredumps, they are the result of a unix program crashing and then getting it's core dumped, which is basically a file containg what the program was doing when it crashed (memory state and CPU state).

If you have that many, it might be a symptom of a bigger underlying cause which you can check by inspecting the logs of you system using the Console app. To find out what binary (application program) the core belongs to, you can use the Terminal:


Open Terminal.app
Type "file " (excluding the quotes but keeping the space at the end) 
Drop a core file on the terminal window, and it's full path will be entered
Press enter and the response will tell you all readable details on the file


In the end, however, unless you are a software developer, there is no point in keeping those core dump files, you can simply delete all of them.