there's a number of causes for this, you're using a PNG which works great in photoshop but many browsers have trouble with rendering the translucency effects.
More importantly, matting. When you save as for web you have to pick the appropriate matte, which in photoshop doesn't matter but once exported makes all the difference. The default matte is white, you need to change it to black, or any other color you prefer. You can try no matte, and for PNGs it's fine (albeit still troublesome in certain browsers) but for gifs it will just solidy anything with alpha>50% and clear anything with alpha<50%
hope that helps, lmk if you need anything else. PM will get me to respond quicker, feel free to contact me.