Segmentation fault (core dumped) - to where? what is it? and why?

If other people clean up ...

... you usually don't find nothing. But luckily Linux has a handler for this which you can specify at runtime. In /usr/src/linux/Documentation/sysctl/kernel.txt you will find:

[/proc/sys/kernel/]core_pattern is used to specify a core dumpfile pattern name.

• If the first character of the pattern is a '|', the kernel will treat the rest of the pattern as a command to run. The core dump will be written to the standard input of that program instead of to a file.

(thanks)

According to the source this is handled by the abrt program (that's Automatic Bug Reporting Tool, not abort), but on my Arch Linux it is handled by systemd. You may want to write your own handler or use the current directory.

But what's in there?

Now what it contains is system specific, but according to the all knowing encyclopedia:

[A core dump] consists of the recorded state of the working memory of a computer program at a specific time[...]. In practice, other key pieces of program state are usually dumped at the same time, including the processor registers, which may include the program counter and stack pointer, memory management information, and other processor and operating system flags and information.

... so it basically contains everything gdb ever wanted, and more.

Yeah, but I'd like me to be happy instead of gdb

You can both be happy since gdb will load any core dump as long as you have a exact copy of your executable: gdb path/to/binary my/core.dump. You should then be able to continue business as usual and be annoyed by trying and failing to fix bugs instead of trying and failing to reproduce bugs.

Also, if ulimit -c returns 0, then no core dump file will be written.

See Where to search for the core file generated by the crash of a linux application?

You can also trigger a core dump manually with CTRL-\ which quits the process and causes a core dump.

The core file is normally called core and is located in the current working directory of the process. However, there is a long list of reasons why a core file would not be generated, and it may be located somewhere else entirely, under a different name. See the core.5 man page for details:

DESCRIPTION

The default action of certain signals is to cause a process to terminate and produce a core dump file, a disk file containing an image of the process's memory at the time of termination. This image can be used in a debugger (e.g., gdb(1)) to inspect the state of the program at the time that it terminated. A list of the signals which cause a process to dump core can be found in signal(7).

...

There are various circumstances in which a core dump file is not produced:

   *  The process does not have permission to write the core file.  (By
      default, the core file is called core or core.pid, where pid is
      the ID of the process that dumped core, and is created in the
      current working directory.  See below for details on naming.) 
      Writing the core file will fail if the directory in which it is to
      be created is nonwritable, or if a file with the same name exists
      and is not writable or is not a regular file (e.g., it is a
      directory or a symbolic link).
   *  A (writable, regular) file with the same name as would be used for
      the core dump already exists, but there is more than one hard link
      to that file.
   *  The filesystem where the core dump file would be created is full;
      or has run out of inodes; or is mounted read-only; or the user has
      reached their quota for the filesystem.
   *  The directory in which the core dump file is to be created does
      not exist.
   *  The RLIMIT_CORE (core file size) or RLIMIT_FSIZE (file size)
      resource limits for the process are set to zero; see getrlimit(2)
      and the documentation of the shell's ulimit command (limit in
      csh(1)).
   *  The binary being executed by the process does not have read
      permission enabled.
   *  The process is executing a set-user-ID (set-group-ID) program that
      is owned by a user (group) other than the real user (group) ID of
      the process, or the process is executing a program that has file
      capabilities (see capabilities(7)).  (However, see the description
      of the prctl(2) PR_SET_DUMPABLE operation, and the description of
      the /proc/sys/fs/suid_dumpable file in proc(5).)
   *  (Since Linux 3.7) The kernel was configured without the
      CONFIG_COREDUMP option.

In addition, a core dump may exclude part of the address space of the process if the madvise(2) MADV_DONTDUMP flag was employed.

Naming of core dump files

By default, a core dump file is named core, but the /proc/sys/kernel/core_pattern file (since Linux 2.6 and 2.4.21) can be set to define a template that is used to name core dump files. The template can contain % specifiers which are substituted by the following values when a core file is created:

       %%  a single % character
       %c  core file size soft resource limit of crashing process (since
           Linux 2.6.24)
       %d  dump mode—same as value returned by prctl(2) PR_GET_DUMPABLE
           (since Linux 3.7)
       %e  executable filename (without path prefix)
       %E  pathname of executable, with slashes ('/') replaced by
           exclamation marks ('!') (since Linux 3.0).
       %g  (numeric) real GID of dumped process
       %h  hostname (same as nodename returned by uname(2))
       %i  TID of thread that triggered core dump, as seen in the PID
           namespace in which the thread resides (since Linux 3.18)
       %I  TID of thread that triggered core dump, as seen in the
           initial PID namespace (since Linux 3.18)
       %p  PID of dumped process, as seen in the PID namespace in which
           the process resides
       %P  PID of dumped process, as seen in the initial PID namespace
           (since Linux 3.12)
       %s  number of signal causing dump
       %t  time of dump, expressed as seconds since the Epoch,
           1970-01-01 00:00:00 +0000 (UTC)
       %u  (numeric) real UID of dumped process