Every word in Arabic derives from 3 root letters. Forms in Arabic are a way of modifying these roots to create new words whose meaning is based on the original one. For example, one might turn a verb like "help" into the verb "cooperate", which carries the connotation of working in groups. Thus, essentially each verb in Arabic can be modified from its original root to make a new word with a different meaning.
How is this different from the role cases play in languages that rely strongly on cases (such as German, Polish, and Russian)?
In English, I thought an example of a case was I versus Me. Me denotes an object while I denotes a subject. Obviously, I and me sound nothing like. So in that sense, cases and forms are very different. But a similarity is that changing / modifying the word yet retaining the original meaning to some extent. Although I and Me are not the same kind of word, both refer to the same person. Similarly, both cooperate and help are related to the same general idea of performing positive, constructive actions.
Perhaps these concepts are unrelated but I was hoping someone could clarify why a bit so that I can better understand what exactly a "form" is in Arabic.