Form in linguistics and language refers to the symbols used to represent meaning. Each form has a particular meaning in a particular context. This cannot be stressed enough. It implies that a form can have different meanings in different contexts. However, the range of meanings for a form is usually limited to a prototype or prototypes based around an image schema to a set of extensions. This is referred to as polysemy (think of the different meanings listed in a dictionary of a particular word).
Note that the relationship of the form to meaning is largely arbitrary. This is quite easily proven to be true. Firstly, if meaning is linked to form then naturally all languages will have the same form for the exact same meaning. This is obviously not true by observation of any two language. Secondly, meaning changes over time for a form. An example of this is ‘gay’. Two hundred years ago this word had meant ‘happy’. Today it signifies a social group. Furthermore, ‘gay’ no longer has negative connotations that it did just 30 years ago.
But in linguistics, it is not form and meaning but form-meaning, one word. The proper terms used for form-meaning, form and meaning are sign, signifier and signified respectively.
Finally, signs can represent either real things or imaginary concepts. As long as these things or concepts are considered coherent they can be given a form, and turned into a sign by a language community.