Is this a bike light and how do I turn it on? (I know it sounds stupid) I've been doing a lot more cycling in the last year since moving to a new town and have really enjoyed it. 

I had a fairly crappy bike though and went to a secondhand store quite far away to get a good bike at a nice price. 

One big issues is there is what I assume is the bike light in front of it (just one) but I see no way to get it to actually turn on, which means I can barely cycle now. 

I used to have the lights where you move that part down to touch the wheel and the movement causes the light to go on (best way I can explain it). This doesn't do that. I also don't see any on/off button or basically any obvious way to get it to work. The store I bought is really far away as are the good bike stores (I live in a small town.)

I've started to wonder if it's really a light or a reflector - although it looks like the former. Any help please?
This is a halogen light. Such lights are usually powered by a bottle dynamo. That is a small electric generator that is driven by the front or the rear wheel. There is usually no switch. One simply engages the dynamo by pushing it down, such that a spring presses it against the flank of the tyre.

Some bikes have a hub dynamo instead. In this case there might be a small switch at each light. A hub dynamo looks like a very large front hub (central part of the wheel).

If you have such a dynamo make sure that the light is connected to it. Follow the wires from the lamp to the dynamo. On older bicycles with bottle dynamos there is typically only one wire. The bicycle frame serves as common ground connection.

Check if the dynamo is properly pushed to the tyre and that its wheel spins when you spin the tyre.

The bulb in the lamp might be defective or missing. Replacement bulbs are not very expensive. But they may be hard to find today. An inexpensive led lamp might be a better replacement, as such lamps are considerably brighter.

Finding the fault may be a little tricky without a volt meter or other means to test electrical connections. If you cannot got to a bike shop anyone who is handy with simple electrics may help you out. For example, electricians or car mechanics.