Until the killer gets to the Ir Miklat (city of refuge), the Go'el Hadam (blood avenger) can kill him, and the killer is in danger. So the Mishnah tells us that we have certain halachot (laws) that were there to help protect the killer. We don't want bloodshed.
The roads that led to the Ir Miklat were straight. They went directly there; they weren't curvy, so the killer could get there quickly. He could reach the Ir Miklat without getting caught by the Go'el Hadam, and the road gave him safe passage there. There were no curvy roads, and at every turn or crossroads, there was a sign that said Miklat (refuge) in every direction.
We're going to learn in the next Mishnah that they would put the killer on trial just to determine whether the killing happened b'shogeg (unintentionally). But before it was determined whether he did it b'shogeg, the Go'el Hadam was not allowed to kill him. But if he did, he would be patur. He wouldn't get in trouble for it. So even at this point, before the trial, there's a good chance that the Go'el Hadam is going to come after him. So right away after he kills b'shogeg, the recommendation is that he runs to the Ir Miklat.
And we learn here that there was a road direction, as the Pasuk (verse) tells us about the Ir Miklat: “Prepare a road for yourself and divide the land.” This tells us that we have to prepare the road to the Ir Miklat so that the killer can get there quickly.
Like we mentioned, we're going to learn in the next Mishnah that after the killer gets to the Ir Miklat, the court would bring him in and put him on trial to see if he was actually required to go into exile. If they eventually say that he was b'shogeg and the killer then has to return to the Ir Miklat, the hachamim, two rabbis, want to make sure that he's protected on his journey back. Because technically, the Go'el Hadam could kill him until he gets there. So the court provides the b'shogeg killer with two hachamim, two rabbis who escort him all the way to the Ir Miklat. We suspect that the Go'el Hadam is going to come try and get him on the way. The Go'el Hadam knows that once the murderer gets to the Ir Miklat, the murderer is out of reach, and the Go'el Hadam can't kill him. So we assign two rabbis. And what are the rabbis going to do? They're going to talk to the Go'el Hadam and try to convince him to spare the killer's life. Even though the Go'el Hadam has the rights and the permission to kill, the Torah, of course, frowns upon it. Therefore, they want the rabbis to discourage the Go'el Hadam from taking his revenge.
Rabbi Meir disagrees. Rabbi Meir says, “No, we don't have two hachamim speak for the killer. Af hu medaber al yedei atzmo.” The killer speaks for himself to the Go'el Hadam and should plead for his life. You don't have the rabbis do it. Like the Pasuk tells us when talking about this: “Vezeh devar harotzeach.” This is the matter. The word devar here means matter, but it also means dibur (the word of the killer). So we see an allusion here to the fact that the killer is going to speak up for himself.