You forgot to tell grep where to search, so it just sits there waiting for data to be input from 'stdin' – often a pipe, but in this case your keyboard. You can confirm by entering something like "this is a word", Enter, CtrlZ, Enter.
If you want to search the current directory, recursively, give . as the path.
grep -rne word .
In many cases, * will work too, but it is not recommended because 1) it is inefficient – expanding the wildcard to all file names takes some time and might even overflow the permitted command line length; 2) it does not match dotfiles (names starting with a dot) in most shells, although I'm not sure if this applies to expansion done by Cygwin itself.
