What does the information on DSLR lenses such as the mm range and the f/stop mean in terms of filmmaking, specifically relating to depth-of-field. Lenses are the only aspect of filmmaking I don't understand and I want to be able to make informed decisions about them.
They mean the exact same thing they do in the photography context. The mm measurement is the focal length. It determines the angle of view the lens produces (ie, how "zoomed in" it appears.) Lenses with a range are zoom lenses where the angle of view can be adjusted. "Zoom" is otherwise not a meaningful thing. Optically, zoom just means you can change the focal length. The x numbers associated with consumer zoom lenses are meaningless as they just describe the relationship between the smallest and largest focal length, not how much magnification a lens provides.
f/ numbers are measurements of how far the aperture of the lens can open. The smaller the number, the more light the lens lets in and the smaller the depth of field is. If there is a range of f/ numbers, it means that the lens' maximum aperture (the smallest number it can go to) changes over the focal length range of the lens. Generally, the largest aperture (smallest f/ number) will be at the wide end (the smallest mm number) and the smallest (largest f/ number) will be at the telephoto end of the lens (largest mm number). This can actually be a desirable feature to have on lenses used for video as it allows for smooth lighting and depth of field adjustments on the fly without needing to use third party firmwares to make smooth adjustments from the camera.
On many modern lenses, the f/ selection is done on the camera and the aperture is electronically adjusted. There are, however, lenses that include manual aperture rings that include both notched and unnotched aperture values (ie, they either move freely between different aperture values for smooth adjustments to aperture (sometimes called iris in video) or to be able to precisely select specific values.
Note that most photographic zoom lenses will not exactly hold focus as you zoom (parafocal), so that is also something to be aware of when zooming optically with a photographic lens. This is also a big part of why cinema lenses (which are parafocal) cost so much more than similar quality photographic lenses. You can do just fine using a good photographic lens that is nearly parafocal, you just need to remember to make focus adjustments along with your zooms.