Bokeh is formed by many points of light spreading out, passing through the aperture and being projected onto the image plane as series of overlapping discs (assuming a round aperture).

This can lead to harsh textures and effects when there are strong contrasts in the out of focus parts of an image, especially when lenses feature overcorrected spherical aberration (required for sharp rendering at the plane of focus) as this can cause bokeh discs to be brighter at the edge than in the centre. An apodisation element can reverse the effects of SA overcorrection.

An apodisation element is simply a radial neutral density filter (that gets darker towards the edges) placed near the aperture stop. This causes each disc of light to fade out gradually toward the edges. This helps the individual discs blend together to produce much smoother bokeh. The blur you get is effectively the same as running a Gaussian blur over the image.

It would be possible to get a similar effect using a screw in filter on the front of the lens (just like you can get creative bokeh shapes) but it's better done at the aperture stop as this wont increase vignetting.

An alternative for long exposures with lenses that feature a clickless aperture ring is to gradually stop down the lens during the exposure to create bokeh discs which are exposed less at the edges (and therefor darker).

---

One downside is that light is lost in the process so lenses with such elements often transmit 1 or 2 stops less light than the f-stop suggests.

Opinion is divided on the value of such an approach with some feeling the resulting bokeh is too smooth and looks fake (due to the similarity with Gaussian blur, which is sometimes used to fake bokeh in photoshop (before the more realistic lens blur filter became available)).