Hi Yaw, vertices are able to store vertex colours as well as vertex alpha (as well as many other attributes), enabling you to add colour/transparency to a model in a very cheap way...ou might not use this for pre rendered work however it is great for real time application, like in computer games etc
Trevelyan Art exactly what trevelyan said. For movie and commercial rendering you would normally do a separate render pass that is just AO and composited later on. For video games vertex colors can do many things. you can cheaply store ao date(but you can also just bake that into your diffuse map) you can use it for what are called threshold shaders where you paint black and white data and that data goes into a shader and says does it use shader a or shader b. you can also do vertex animation through vertex color where you use the rgba and drive math functions through a shader.
In case anyone get an issue with assigning the vertex colurs, the 3DS Max 2016 Service Pack 1 fixes this :) knowledge.autodesk.com/support/3ds-max/downloads/caas/downloads/content/autodesk-3ds-max-2016-service-pack-1.html