Assuming you do want to "flatten" your vectors then do as Scott says, you can however get the same result non-destructively using a knockout group. Whether you need to do this destructively or not depends on your needs, if you're outputting to a raster format or importing this somewhere where you don't need the path data then this may be a better (easier & more maintanable) option.
Take this vaguely similar construct for example:
Group the logo (You could also put it on it's own layer and use the layer).
Open the Transparency panel for the group and check "Knockout Group" (you may need to click the box twice—so that it has a check mark not a line).
- Select everything with a white fill using the Direct Selection Tool (white arrow — A)
- From the Appearance panel, open the Transparency panel for the white fill (by expanding the "Fill" entry and clicking "Opacity") and set opacity to "0".
If you also have any white strokes, repeat steps 3 and 4 for the strokes.
Your now transparent logo: