When you first start using Adobe Illustrator you will come across the annoying white background.

This background is not part of the image and is possibly called the 'Art Board'.

To remove it there are several options outlined below:

• export as a psd (from ai). This also has the side effect of correctely cropping the image id the background is mismatch for the image/logo. The PSd has layers and seem to match up well with the objects. You can then do what you want including "save for web" which allows you to save it as a PNG with transparency
• "save for web" - this is the simplisted method but does not crop the image if mismatched to the background
• shift+CTRL+D - How to Make Adobe Illustrator Background Transparent | BudgetVideo4BIZ Blog