What does MF do on my Z3?

Pardon me for my ignorance:

I press the up button on my Z3 and it cycles between Macro, infinity, and MF. I assume that MF stands for Manual Focus. When I set the camera to MF, I notice that there is a considerably shorter delay in shutter lag (time presing shutter til time image captures)

I also noticed that the camera does not seem to do any focusing while in MF, so how does this mean Manual Focus? A yellow box appears and I don't know what that box means.

Someone please help?! thanks.