Many digital cameras support to store images as they are recognized by the sensor. These images are not compressed and contain more bits per pixel which allow more adjustments with lesser artifacts. To use RAW images in your regular workflow wasn't easy in the early days, but nowadays they should be supported by any major photo editing software.

Source JPG-File (normal).

Source NEF-File.

For general images you normally won't need a RAW-format. When you target the computer's screen or small prints, don't bother with their more complex handling.

But there are some situations, when using a RAW-format results in obviously better images.

One advantage of a RAW-file is the higher color bit-depth per pixel. Contrary to JPG-files NIKON-NEF-images store 12 Bits per color-channel. This allows modifying whitebalance and exposure during import and gives you much more freedom when making color and contrast adjustments. My night-shots are mostly taken in RAW-format for these reasons.

RAW-files normally have no or at least a lossless compression. If you really need the last bit of resolution, there's probably no way except using a RAW-format. The D70 for example uses a size-based quality-setting for JPEG-files, so the resulting file-sizes are largely constant. When image-complexity increases, like within the trees above, you'll just loose resolution and definition.

If you still prefer using JPEG-files, a compression set to normal is sufficient for most images. But then you should not forget to switch to fine quality, when image details increase.