The 'c' means it's a character device. tty is a special file representing the 'controlling terminal' for the current process.
Character Devices
Unix supports 'device files', which aren't really files at all, but file-like access points to hardware devices.
A 'character' device is one which is interfaced byte-by-byte (as opposed to buffered IO).
TTY
/dev/tty is a special file, representing the terminal for the current process. So, when you echo 1 > /dev/tty, your message ('1') will appear on your screen. Likewise, when you cat /dev/tty, your subsequent input gets duplicated (until you press Ctrl-C).
/dev/tty doesn't 'contain' anything as such, but you can read from it and write to it (for what it's worth). I can't think of a good use for it, but there are similar files which are very useful for simple IO operations (e.g. /dev/ttyS0 is normally your serial port)
This quote is from http://tldp.org/HOWTO/Text-Terminal-HOWTO-7.html#ss7.3 :
/dev/tty stands for the controlling terminal (if any) for the current
process. To find out which tty's are attached to which processes use
the "ps -a" command at the shell prompt (command line). Look at the
"tty" column. For the shell process you're in, /dev/tty is the
terminal you are now using. Type "tty" at the shell prompt to see what
it is (see manual pg. tty(1)). /dev/tty is something like a link to
the actually terminal device name with some additional features for
C-programmers: see the manual page tty(4).
Here is the man page: http://linux.die.net/man/4/tty
