An understanding of form and function is a variation on the "knowing what vs. knowing how" discussion:

Form refers to the name of a thing (along with its definition) 

Function refers to how a thing is acting or operating in a particular context.

When analyzing grammar in this textbook, understanding the difference between FORM and FUNCTION is one of the keys to successful analysis of words, phrases, clauses, and sentence in their context.

To begin, our language can be seen as layers upon layers, and we can analyze our language from a variety of perspectives, for a variety of reasons. So the first point to remember is that you can identify, or name, a FORM at the word level, at the phrase level, and at the clause level. Similarly, you can also analyze how each FORM is FUCTIONING in the context of a sentence (or passage). Once again, you can identify the FUNCTION of a FORM at the word level, at the phrase level, and at the clause level.

FORM names things at the WORD level (noun, verb, adjective, adverb, preposition, relative, etc.), at the PHRASE level (main verb phrase, prepositional phrase, present participle phrase, past participle phrase, gerund phrase, infinitive phrase, etc.), and at the CLAUSE level (independent clause, dependent clause, subordinate clause, relative clause, nominal clause, etc.). There are lots of FORMS, but a finite number of FUNCTIONS.

In fact, there are only four (4) FUNCTIONS: 

1. nominal - a noun or any group of words that can substitute for a noun (word, phrase, or clause) and perform nominal functions. In other words, they can do anything that a noun can do, including filling any of the common nominal slots in a sentence (subject, direct object, subject complement, or object of the preposition most commonly).
2. adjectival - an adjective or any group of words that can substitute for an adjective (word, phrase, or clause) and perform adjectival functions. In other words, they can do anything that an adjective can do (modify nouns or nominals most commonly).
3. adverbial - an adverb or any group of words that can substitute for an adverb (word, phrase, or clause) and perform adverbial functions. In other words, they can do anything that an adverb can do.
4. main verb phrase (MVP) - the main verb of a clause plus its auxiliary or helping verbs in an unchanging order.

As we will discuss throughout Analyzing Grammar in Context, whether a FORM is defined at the WORD level, the PHRASE level, or the CLAUSE level, we have formal tests for determining FORM and functional tests for determining FUNCTION. In most cases, FORMS will only take one of the four FUNCTIONS listed above. There are a few notable exceptions to this rule (structure-class words and independent clauses, for example); in other words, while the form and function of a form-class word is normally the same (noun functions nominally, for example), form-class words can also function differently from their form. In other words, a noun may function adjectivally, like BASEBALL BAT or TENNIS SHOES. On the other hand, the Form and Function of a structure-class word is always the same. For example, a determiner can only function as a determiner; a preposition can only function as a preposition, and we will cover these explicitly in Sections 4-6. Moreover, we will describe how some FORMS can only FUNCTION in certain ways, while other FORMS can FUNCTION in multiple ways. 

To summarize, we analyze for FORM (name something), but, more importantly, we also analyze to determine how a FORM is FUNCTIONING in a particular context.