Hello,
This happens because the edges of the image need to gently transition into the background colour. In this example Photoshop has assumed that the background will be white, so it has faded the edges towards white.
To solve this you need to use the matte feature. When you select "Save As" you will see a window like the one on the bottom. Select the Matte drop-menu, then select Custom. A colour-picker window will appear — enter the colour of your background.
In our example we will use the colour #292929 (for forum).
Continue to save the file. If all goes well, it should now blend nicely into the background.