The guide bushing is a bearing on a Swiss-type (sliding-headstock) CNC automatic lathe that supports the bar stock immediately next to the point where the tool cuts.
Because the material is machined while passing through the guide bushing, it is supported close to the cutting edge and resists deflection.
A Closer Look
In turning, the longer the distance between the point where the material is supported and the cutting edge, the more the cutting forces deflect the material and degrade precision.
The effect is especially pronounced on long, slender parts.
By supporting the material right next to where it is being cut, the guide bushing suppresses this deflection and makes high-precision machining possible even on long, slender workpieces.
This is why the Swiss-type is said to be "strong on slender, high-precision parts."
Using a guide bushing does have trade-offs — a somewhat longer remnant and tighter demands on bar diameter accuracy — so for some applications a configuration without a guide bushing is chosen instead.