The fermentation is relatively complex, as quite a number of different bacterial species and yeast live in the Kefir grains. These are made of of the polysaccheride kefiran which immobilizes the bacteria (in contrast for example to yoghurt). The microbes live symbiotic on this matrix.
According to the references a number of different microorganisms has been found, these include mainly Lactic acid bacteria, followed by yeasts and acetic acid bacteria. The species include: Lactobacillus paracasei, Lactobacillus parabuchneri, Lactobacillus casei, Lactobacillus kefiri, Lactococcus lactis, Acetobacter lovaniensis, Kluyveromyces lactis, Kazachstania aerobia, Saccharomyces cerevisiae and Lachancea meyersii.
In brief the lactobacilli break down lactose to produce lactic acid, while the yeasts make alcohol and carbon dioxide while the acetobacter species make acetic acid. This consumes the lactose and the fat content of the milk making it suitable for lactose intollerant people. It also lowers the pH of the kefir. The exact mixture is hard to identify as this contains strongly on the exact composition of the kefir grains.
If you are interested further, I recommend you have a look into the references, I find both articles relatively good to understand.