The picture is downloaded in full, but the forum software generates size parameters which tell your browser to rescale the image.
EG
<img src="
https://lh5.googleusercontent.com/-lrQs91BnFKg/T0p1lDXCzxI/AAAAAAAADlM/BY8wrJhMUw8/s800/DSCF1663.jpg" alt="" width="600" height="450" border="0" />
That's from a post that I made today. The actual size of the picture is 800 x 600, but the forum software is telling the browser to resize it to 600 x 450. The resize calculation seems to happen after you clicke the "post" button.
This doesn't save bandwidth, but it does reduce screen real estate needs, and it may be necessary to keep forum pages properly formatted at display time. Also letting the software control the sizing exerts some control over people posting huge pictures that are likely to fill up a screen or be even bigger if not resized.