The scene is rarely shown on stage, so Shakespeare wanted to leave it a mystery.
In Roman Polanski's film Macbeth, the third murderer is Ross. Polanski has him arrive late on the scene on horseback. As Fleance escapes on his horse, Ross draws his sword and is about to kill the boy, but Banquo shoots Ross' horse with an arrow. Banquo gets the ax to the back, but Ross is thrown from the horse and Fleance escapes.
I do like this interpretation, as Ross seems also complicit in Lady Macduff's murder. He in the scene preceding, warning hers to leave. Ross is omnipresent to all the murder and bloodshed in the play.
That is a question that has plagued Shakespeare fans for centuries. There is no clear reason for the third murderer and there is no previous indication that there should be a third. When Macbeth hires the murderers in Act 3, sc. 1, there are only two. When the murderers meet at the place where they plan to encounter Banquo and Fleance, there are three. Looking carefully at the opening lines of that scene, we get the only clues to reason for the third man. The first murderer asks the third who asked him to be there. The third murderer says simply, "Macbeth." The second murderer then says that Macbeth didn't need to doubt them; they are trustworthy and they will do as they were hired to do. That brief exchange suggests that Macbeth, who is becoming increasingly paranoid, doesn't trust the killers he hired to kill someone he no longer trusts. Macbeth's guilty conscience and his paranoia are what allow him to see the ghost of Banquo in the following banquet scene. His paranoia is what sends Macbeth back to the Weird Sisters in Act 4, sc. 1. By the time we get to Act 5, we see that Macbeth has been driven nearly insane with paranoia as he tries to hang onto the throne in the face of all the odds against him. Macbeth most likely hired the third murderer to check up on the first two and this is done to show the audience Macbeth's increasing paranoia.
This certainly is a mystery. It seems that by sending a third murderer, Macbeth wants to be certain that all goes as planned, but as we see it doesn't, for Fleance is able to flee.
But I once read somewhere that in a play sometime ago the third murderer was played by Macbeth incognito. Imagine Macbeth showing up. It is plausible, for the murder occurs just a mile out from the castle, and when the murder occurs, the three split up and vanish into the dark perhaps in separate ways. Being only a mile out would give Macbeth time to return to the party to attempt "to beguile time" once again.
This would prove to be interesting; it would explain why he is able to see Banquo's ghost at the dinner party.