Some good explanations here about how hey work and how they control stray light. However, some lower-end refractors have baffling that does indeed clip the aperture. I'm not sure why they are designed that way, other than to mask the outer edge of the lens, where the majority of optical issues occur.
The baffles also set what's called the fully, 100%, illuminated field at focus.
A neat and informative thing to do is to note the focuser position when looking at astro-stuff. During the day, run the focuser to that position and remove the eyepiece, then, simply put your eye right up to the opening and look inside the tube. You should be able to see the edges of the objective. Now pan right to left a bit You will more than likely see the edges of at least one baffles start to intrude on the edge of the objective. That "diameter" before that happens is your fully illuminated field. In modern, fast APOs, especially those for imaging, that diameter can be very large. For slower, more visual scopes, that diameter may be rather small but you will also notice that, even when you position your eye all the way over to one side, not that much of the objective is masked. The other thing you will see is just how deep black the blackness surround the objective is. Even simple baffling is very, effective at killing off stray light.