Many people use polishes on their furniture. If there is a sufficient amount of finish on your piece there is no need for polishes. I hear all the time from people that the finish on their furniture looks dry and they polish it to feed the wood. Chances are, if your furniture looks dry, the finish is so thin that there is hardly a film there. You don't feed the wood if your furniture has a finish on it. When I save a finish or refinish a piece, all you need to do is dust the piece. You can use a product, such as Endust® by spraying a little on a soft cotton cloth (an old t-shirt works well) and dust the piece wiping with the grain. Wipe with the grain of the wood because there could be a fine piece of grit on the surface which could scratch the finish. A scratch with the grain will hide much better than a scratch across the grain.
If you do use a polish, do not use one with silicon. It should be listed on the can. Silicon is bad, as it contaminates the finishes. It is an oil, which if it get on the surface, or worse, into the grain of the wood, it can contaminate it. When it is contaminated, it looks like little dimples all over the surface. This will not show up until you go to add more finish to the piece or refinish it. There are techniques to get past it but, sometimes, when you try to save a finish it can be so bad, that the piece will have to be stripped.
I have heard stories that even someone using a common furniture polish with silicon in it in another part of a room, contaminated another piece of furniture at the opposite end of the room. Just the air borne particles can contaminate the surface.
So, if you must use a polish check the label first. Most polishes have some sort of oil in them and that is why furniture looks good for a couple of days. Then the oil evaporates and you are left with it looking like it looked before. If you have a finish that is good shape, all you will need to do is dust it.