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Wood-veneer cabinets are constructed of plywood, particle-board or some other cheap substance, then overlaid with a very thin layer of oak or other finish wood to give it the appearance of being solid wood. The surfaces of these cabinets are real wood, but they generally can't be sanded down for staining, because you risk taking off the veneer and exposing the sub-material. However, veneer surfaces can be re-glossed, which is often enough to brighten them up and provide a new look.
Remove the cabinet doors and set them on newspapers on the floor. Remove all hinges and hardware with a screwdriver and set it aside.
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Lightly sand the entire surface of the cabinets and doors with 100-grit sandpaper. Sand it just enough to take off the shine of the old gloss, without going all the way down to the wood surface. Wipe the sanding dust off everything.
Starting at the top of the cabinets, use your brush to apply a light layer of gloss to the wood. Brush with the grain of the wood in short, slow strokes, avoiding drips and bubbles. Let it dry for a day.
Lightly buff the new gloss with 120-grit sandpaper, just enough to take off the shine. Apply a second coat of gloss in the same manner as the first. Let it dry.
Apply a third coat in the same way, buffing the gloss and brushing on a thin, new layer. After it dries, put the cabinet doors and hardware back on.
If you're not sure whether your cabinet is solid wood or veneer, examine the edges and corners inside the doors and under the cabinet; look for tell-tale lines where the veneer meets the material beneath.
Make sure a window in the room is open during the glossing, to provide ventilation.