File size versus image quality. The age old (computer age) trade off when dealing with image files. To reduce the file size you simply have to lose some of the image quality. There really is no way around this fact. But there are means within this limitation that we can work with. And one of them is called "weighted optimization".
What it means is you can reduce the image quality while influencing specific portions of the image to be more or less affected by that quality reduction.
Two commonly used methods of reducing file size are to convert to a GIF (which uses a reduced color palette of 256 colors or less) or convert to a JPG (which uses a form of lossy compression as well as color reduction of it's palette). When saving to either one of these formats from Adobe Photoshop it's possible to influence the quality reduction involved and have it weigh more heavily on some parts of the image and less so on other parts. This "weighted optimization" can be handy in things like banners or other images that involve text because it is vital to keep that text readable, or it can be used in any image where you'd like to keep a specific portion of the image looking as good as possible.
To use this feature of Photoshop you must first define a mask and save it. You want the mask to consist of the area of your image that you are least concerned about quality. So in essence just select the important parts of the image that you'd like to be least affected by quality reduction, then choose "selection", "inverse", then "save selection".
For example, let's say I wanted to convert the following image to a GIF file (with a reduced color palette) yet I wanted the border around the yellow area (that raised 3D looking black/blue border) to remain looking as good as possible. Maybe in the big picture that blue/black border is part of some larger text or logo.