A somewhat obvious case is this:

   .                                                                                                              
   ├── subdir                                                                                                     
   │   └── test2.dat                                                                                              
   └── test.dat                                                                                                   

   1 directory, 2 files

If you don't use double quotes then the shell will expand test* to be test.dat and the final command will actually be:

  find . -name test.dat

...so the file named "test2.dat" in the sub-directory therefore won't be found.

Instead of using double quotes you can escape the asterisk so it won't be processed by the shell, e.g.

   find . -name test\*