The ignited sabers used spinning sticks with reflective tape covering them, and some rotoscoping applied in post to get the final effect. There are spots in the un-retouched Star Wars where the effect is missed, or something, and you can indeed see the raw stick. Something similar's also behind that one weird shot where Obi Wan's saber seems to almost fizzle out (the tip is pointed too much toward the camera, and messes up the effect)

The careful eye may also notice they almost never strike the sabers against one another in that scene... because it'd break the spinning sticks. Apparent contact is usually gently done, or a trick of perspective.