If you are working on a single paper and moving between different computers, it is best to keep a copy of your reference library with your paper. That way you will always access the same library when inserting citations. If you separately add references to a copy of the library at home and to a different version at work, record numbers may not match up correctly and EndNote may have to rely on the Traveling Library for reference information. That is not necessarily bad, but you want to make sure that any library edits are reflected in your Word document.
If you are inserting citations on only one machine, it is fine to move the document itself to other machines—as long as you will be accessing the document with the same version of Word.
Note: If you are collaborating with other authors, you will want to rely on the Traveling Library.