What does the command “chattr +c /some/dir/” do

The a attribute means that the file is append-only: you can't overwrite it or delete it, only append data to it. This is explained in the chattr man page. Only root can remove the attribute.

The practical consequence is that you can't erase your old history lines. This is presumably intended as a security measure by your system administrator. I'm not completely convinced it's secure, but off the top of my head I can't think of a way to remove some of the file's contents. (It is however easy to bypass the file and run commands without their showing in the history, which is why it's not a particularly useful security measure against competent users — an obvious way being to run the commands from something other than bash.).

  The  letters  `acdeijstuADST'  select the new attributes for the files:
  append only (a), compressed  (c),  no  dump  (d),  extent  format  (e),
  immutable (i), data journalling (j), secure deletion (s), no tail-merg‐
  ing (t), undeletable (u), no atime updates (A),  synchronous  directory
  updates  (D),  synchronous  updates (S), and top of directory hierarchy
  (T).

from the manpage for chattr

Files with this flag will fail to be opened for writing. This also blocks certain potentially destructive system calls such as truncate() or unlink().

$ touch foo
$ chattr +a foo
$ python
> file("foo", "w") #attempt to open for writing
[Errno 1] Operation not permitted: 'foo'
> quit()
$ truncate foo --size 0
truncate: cannot open `foo' for writing: Operation not permitted
$ echo "Appending works fine." >> foo
$ cat foo
Appending works fine.
$ rm foo
rm: cannot remove `foo': Operation not permitted
$ chattr -a foo
$ rm foo

This option is designed for log files.