I've always thought this was an interesting phrase to use here. As you've already read, this line specifically refers to Tom Robinson's desperate--almost animalistic--attempt to escape his desolate and hopeless future.
Isn't it ironic that these same words, in a different context, might describe the accusation against Tom--"a blind, raving charge."
"Blind" - Mayella has to shift the blame to Tom, and her father (Bob Ewell) accuses him blindly (which is different than randomly).
"Raving" - a perfect description of both Mayella's and Ewell's accounts of the crime Tom supposedly committed.
"Charge" - the obvious cause for the trial.
I certainly don't want to replace the literal meaning of the phrase as it is applied to Tom's death; I think it's simply something interesting to note, since you're looking at it.
The implications of this phrase are very stereotypical. By some, remarks were made that compared the behavior of black men to that of animals. In this phrase, Tom Robinson's actions are metaphorically compared to those of a creature such as a bull, that cornered, would become so frightened and enraged that it would be filled with a rush of adrenaline, causing it to be unthinking and simply react with its force to try to charge out of its confinement--"blindly" going it knows not where--simply fleeing. Poor Tom feels trapped, much like an animal caged. His flight instinct takes hold of him; his reason tells him he will be hanged. He unthinkingly gives in to his flight instinct and tries to run. Sometimes, this reaction is called "turning rabbit."
So are you just asking what this phrase means? It is referring to what Tom Robinson did when he tried to escape from the prison. It simply means that he ran in a wild manner towards the fence.
The word "blind" implies that he was not really thinking or paying much attention to what he was doing. The word "raving" has to do with his state of mind as well. To be "raving" means to be somewhat crazed. So the author is saying that Tom Robinson was crazed and was not thinking as he charged (a word meaning to run, but with a more aggressive nuance to it) towards the fence.
Overall, then, the meaning of this is that Tom Robinson was not thinking clearly when he ran towards the fence of the prison and was killed.