The image posted in this forum is a JPEG of a CMYK image with white background, and JPEG is always opaque. You'll want to export an RGB image for a website, and most likely, one that's been converted to sRGB profile. If you want a PNG file without tranparency then use File > Save For Web, pick PNG-24 and clear the Transparency checkbox.
I finally did notice and learned something new that you can not use CMYK for website.
I didn't say that you "can not use CMYK for website".
Your CMYK image on this forum page is displayed correctly in my browser, for example.
I did say to use RGB, though.
.... you can not use CMYK for website.
I guess it depends on your browser, this is how I see it in Firefox - I don't see any black background. Bur regardless of this, you should only use RGB for web unless the CMYK image has additional purpose other than just being viewed.
When I changed to RBG it was viewable on the website.