The conflict between Cory and his father Troy is understood by each man differently. The idea expressed in the struggle between the father and son is connected to this difference in perspective, to some degree, and also hinges on the twin ideas of accepting others and accepting the past in order to live a life in the present (and so not remain trapped in the past).
To offer a brief synopsis of the meaning of the conflict between these characters, we might start at the end of the story and look at how the conflict is resolved.
Cory finally agrees to attend Troy's funeral, singing Troy's song about Old Blue with Raynell, his half-sister (from Troy's adulterous affair). In this moment, Cory comes to hold a balanced view of his father, which is to say that he develops the capacity to see the good along with the bad.
In finding a way out of the reductionist tendency that had previously shaped his view as a black-or-white, judgement-laden perspective, Cory is able to rise above the pain of the relationship. He is no longer harmed or haunted by strife with his father. We can imagine that with his own children the cycle of father-son conflict will be broken (and has already been lain to rest).
This sense of history repeating itself is at the heart of the conflict, but, arguably, it is not quite as personal or individualistic as Cory initially believes.
Earlier in the narrative, Cory claims that Troy is holding him back. When Troy suggests that he has worked hard for Cory but says that he is now "through with doing for [him]," Cory responds with a full articulation of his point of view.
"You ain't never gave me nothing! You ain't never done nothing but hold me back. Afraid I was gonna be better than you. All you ever did was try to make me scared of you."
When Troy demands that Cory quit the football team and forgo a scholarship to college, Cory thinks that Troy is worried his son will surpass his sports prowess--a part of his personal history that he is both proud of and troubled by. The truth is that Troy's baseball history is not one of pure triumph, which might be overshadowed by Cory's, but instead is a complex experience characterized by an interplay of categorical identity (race) and personal ability (personality, strength and weakness).
Cory is perhaps too young or too resentful of his father's overbearing demeanor to see Troy's side of the argument when he claims that sports ambitions can lead to bitterness. Troy claims that he is protecting Cory from that bitterness and from that damaging sense of defeat and unfair (racially oriented) limitations on the potential achievement of a dream.
If Cory is unable to recognize the kind of protection his father is genuinely offering, it is equally true that Troy is incapable of seeing his son as a human being with legitimate desires and strengths of his own. Insisting that his only obligation is to provide food and shelter for Cory, Troy perpetuates a hardness of heart that he had encountered in his own father, demanding an authority in his household that leaves no room for the consideration of his son as anything more than a mouth to feed and a hand to help with the chores.
Fenced in by a life of powerful limitations, Troy feels beset by obligations and constraint. He is not free enough or sufficiently at ease to engage with Cory as an equal or, even, as a person. In many ways, Troy is trapped by the conflicts and struggles of his past (as evidenced by his repeated mentions of fighting with the devil). These struggles play out with his own son and are only overcome when Cory embraces a larger view of his father as a man with flaws and virtues.