Recall that in Photoshop terminology, the base color refers to the pixels of the lower layer while the blend color refers to the pixels of the layer on top. At the left are Adobe's definitions of these two blending modes. Note that if you are using a brush to apply the blend pixels rather than a separate layer, the blend color is the color of the brush.
To paraphrase, in saturation mode, the result will have the saturation of the color you are applying but will retain the hue and brightness of the underlying pixels. You can use this to equalize the saturation of all the areas you paint regardless of their hue or brightness. In hue mode, you can change the basic color while preserving the saturation and brightness of the original color. This may be useful in creating monotones or tinting an image.
We will look at an example of saturation mode first, then a couple of uses of hue mode. Although the examples all use separate layers, you should keep in mind that you can use the brush tool in these modes as well for simple touchup work.