Adjustment layers apply color and tone adjustment to your photo non destructively. This means that rather than making an adjustment directly to your photo, you can create a separate layer that will make those adjustments, leaving your original photo untouched.
Blending mode controls how the layer interacts with other layers. For example, the blending mode "multiply" looks at the color of your layer and multiplies the base color by the blend color. The result is always a darker color. Multiplying with black results in black, multiplying with white leaves the color unchanged.