Strings are the bibtex equivalent to constants in a programming language. Each string is defined with a unique name and a content. Elsewhere in the database, the name can be used to represent the content.
For instance, if many entries are from a journal with an abbreviation that may be hard to remember, such as 'J. Theor. Biol.' (Journal of Theroretical Biology), a string named JTB could be defined to represent the journal's name. Instead of repeating the exact journal name in each entry, the characters '#JTB#' (without quotes) are put into the journal field of each, ensuring the journal name is written identically each time.
A string reference can appear anywhere in any field, always by enclosing the string's name in a pair of '#' characters. This syntax is specific for JabRef, and differs slightly from the bibtex notation that is produced when you save your database.
A string may in the same way be referred in the content of another string, provided the referred string is defined before the referring one.
While the order of strings in your BibTeX file is important in some cases, you don't have to worry about this when using JabRef. The strings will be displayed in alphabetical order in the string editor, and stored in the same order, except when a different ordering is required by BibTeX.