Slide
Using a microscope on low power is important for a number of reasons, with protecting the slide being one of them. Since higher power lenses sit considerably closer to the slide, if the microscope is on a higher power when the slide is brought into focus with the coarse knob, the slide is likely to collide with the lens. This will usually crack the slide and ruin the specimen sample.
Lenses
Similarly, a collision between the slide and the lenses can also damage the lens. Even if the slide collides with the lens and doesn't break, scratches will often be left on the lens. This can obscure the viewing area significantly and usually requires repair before the microscope can be used again.
Oil Lens
Additionally, using the oil lens on the slide first, or using the oil lens without oil will damage the lens. Oil lenses are high enough powered that they require more light to display a specimen (which is why the oil is used). Scratching an oil lens usually requires replacement, since the scratches inhibit light from entering the lens and the specimen will be too dark to view.
Specimen
Using a microscope in low power first is also important for finding the specimen on the slide. Looking through the lowest power displays a greater area of the slide, which eases locating the desired area of a specimen. The microscope can then be adjusted to higher powers, which will result in the specimen remaining in the viewable area. Starting on a high power can make finding the specimen difficult, since small adjustments jump the viewing area significantly.