Yes, that's called a bloom effect. Bloom works by identifying the bright parts of the image, blurring them, and then blending that blurred result back over the original image.
Blur is normally done in two passes, for efficiency: first you blur along the horizontal axis, then blur the resulting image a second time along the vertical axis.
The bloom sample (in the education section on this site) implements exactly that in an easily reusable format, and with lots of tweakable parameters. If you have specific questions about how this works, feel free to ask them here.
Bloom is kind of an advanced effect, though. If you are new to HLSL, it might be better to start with the Sprite Effects sample, and the Shader Series of samples.
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