The effect is called “volumetric lighting” or “volumetrics”, where beams of light strike suspended particles, making the beams of light visible.
Normally, this effect is created on set, or with 3D apps such as Maya, Max, Lightwave or Cinema 4D. After Effects cannot reproduce this effect as well as the 3D apps, but it can fake it somewhat with the aid of third-party plugins:
1. Trapcode’s Shine plugin can fake it if you apply it to an image (or footage) of a bunch of bright dots. However, it only works with a static camera, as it is not a “3D” effect.
2. Trapcode’s Lux should do a better job within AE, but I haven’t tried it.
Both products can be found on the Trapcode site.
Hope that helps,
Steve