You need to save it using an image format that supports the type of transparency that you want. The JPEG format doesn't support transparency at all.
There are two types of transparency, transparency index and alpha channel. The GIF and PNG-8 formats support transparency index, i.e. one of the 256 colors are chosen to represent transparency. That means that each pixel in the image can only be either 100% transparent or 100% solid.
The PNG-24 format support alpha channel. That is transparency value for each pixel, so that it can be anything from 100% transparent to 100% solid (in 256 levels).
If your image has mostly fully transparent or fully solid pixels, you can use transparency index, but if it has a lot of partly transparent pixels, you have to use alpha channel.
Note that older versions of IE has problems displaying the transparency in PNG-24 images correctly.