At the beginning of this scene, Banquo congratulates Macbeth on the witches' prophecy coming true, and he hopes aloud to Macbeth that the witches' prophecy for him will come true also:
"that myself should be the root and father of many kings" (3.1.5-6)
After Banquo leaves, Macbeth worries that "our fears in Banquo stick deep" (3.1.48-49). Macbeth focuses on Banquo's character as a concern, fearing that his attributes would make him a perfect king. With the prophecy of the witches firmly in mind, Macbeth fears the "dauntless temper of his mind" and the "wisdom of his valour," because he perceives Banquo as his true, legitimate competition. Macbeth's insecurity about his position makes him see Banquo as a threat which must be eliminated.
Macbeth is afraid of Banquo for two reasons. Firstly, because he has character traits which Macbeth lacks:
'wisdom that doth guide his valour
To act in safety'.
Macbeth has valour/bravery but his actions, such as the murder of Duncan, are rash not to mention evil. If Banquo were to make a move against Macbeth, the latter fears his combination of sound judgement and bravery would see him come out on top.
Secondly, the witches have said that Banquo's descendants, not Macbeth's, will be kings and this is Macbeth's greatest fear causing him to exclaim:
For Banquo's issue have I filed my mind
Macbeth has murdered the King, and so defiled or destroyed his own inner peace (mind) for nothing, since it is Banquo's descendants (issue) that will be royalty. Banquo is a living reminder of this part of the witches' prophecy which Macbeth is trying to blot out. He must be killed.