The above sentence is nominal sentence, formed by a nominal subject and a nominal predicate; Meaning: the speaker is telling the receiver that his father is generous. The adjective (كريم) [generous] here is a "predicative" adjective telling the status of "my father," and hence "my father IS generous".
Now, if I want to describe "my father" as being generous using an attributive adjective, then I would say (أبي الكريم) [abí-l-karím] -using my own notation here- [my generous father]. Notice how (كريم) becomes (الكريم), by adding a definition article to it (الـ). This is because when adjectives becomes attributive (i.e. attached to the noun and describes the noun), the adjective must follow the noun in gender, number and definition. Adding (-í) to the word (i.e. "my") is a form of definition to the word in Arabic, and hence the word (كريم) has to be defined as well, and hence we add (الـ) to mimic the noun which it describes (أبي).