Many citation styles require that journal titles are abbreviated (e.g. using a journal abbreviation list, like the one of Index Medicus).

Most styles use the same journal abbreviations, but some styles include periods (e.g. J. Cell. Biol.), whereas others omit them (J Cell Biol). CSL 1.0 styles (supported by Zotero 2.1 or newer) can dictate that periods should either be left untouched or stripped from the abbreviation in the “Journal Abbr.” field when generating citations and bibliographies. For this reason, you should store journal abbreviations with periods in your Zotero library.

A planned feature for Zotero is support for abbreviation lists, so that different styles can use different journal abbreviations (e.g. Proceedings of the National Academy of Sciences can be abbreviated as either Proc. Natl. Acad. Sci. U. S. A. or PNAS).