Close file without quitting VIM application?

As already mentioned, you're looking for :bd, however this doesn't completely remove the buffer, it's still accessible:

:e foo
:e bar
:buffers
  1 #h   "foo"                          line 1
  2 %a   "bar"                          line 1
Press ENTER or type command to continue
:bd 2
:buffers
  1 %a   "foo"                          line 1
Press ENTER or type command to continue
:b 2
2   bar

You may instead want :bw which completely removes it.

:bw 2
:b 2 
E86: Buffer 2 does not exist

Not knowing about :bw bugged me for quite a while.

This deletes the buffer (which translates to close the file)

:bd