It is my understanding that in regular conditions when using an SLR camera (No live-view) , the camera lifts the mirror to let the light hit the sensor. But while in Live-View, the mirror is already locked-up, so, at the time you press the shutter button, why the need to lower the mirror, and immediately lift it again just before exposure?
Two possibilities, focusing and metering.
Often when shooting in live view, the mirror snaps down to use the phase detect auto-focus, then snaps back up to take the image and remains up to keep live view going. If your camera supports using only contrast based auto-focus, then you can avoid that cycle.
Similarly, it may want to use the light metering capabilities that are available when the mirror is down, depending on how well the sensor can meter for itself as well.
In either case, it is often a setting that can be adjusted in the menus. I know my 5D Mark iii has a setting that will allow the photo to be taken directly in LiveView without the mirror flipping down.
There is some interesting information about live view sequencing on Canon cameras here:
40D, 50D, 5d11, and 7D has the same operation that does not include the mirror movements. 450D, 500D and 1000D do include mirror operations because of their limited design where it is the same motor for mirror and shutter. You can see when this was written in the models on the list, but the general design strategy seems to be rebels vs semi pro and pro lines. So if you have a Canon camera I would guess it is a rebel and your answer is that it lowers the mirror due to this single motor design limitation.
It might be the same design principles in the other brands, if that's what you have.
If you are using flash ETTL2 it is another story. then it needs the mirror down for the initial preflash metering.
Metering, not focusing. It's the final metering before the exposure is initiated.
Contrast focusing is used in live view, and phase detection is not engaged in the short period of time the mirror is dropped - watch your lens.
Its for metering, plain and simple.