I know this might be a stupid question but, what is a wired router used for? The reason I ask is because I will be working for this company online and they require that I have a wired router. But it's difficult to reach them to ask them why they need it and I don't want to sound dumb so that's why I am here. Please help...just a general answer will do... I just need to have an idea of why they might need me to have it. Thank you.

Oh yeah, I have dsl connection and I only need to use one computer with a headphone set, for this position. Thanks again...

A hardwired router is just a router that is not wireless capable. All computers must be connected by LAN cabling. Being hardwired is less likely to have hacking from outside sources.

Using a hardwired router verses a wireless connection is a security issue as well as a tech issue.
hardwired is less likely to be hacked or have a broken connection that sometimes occurs with wireless connectivity. If you are to join a domain's network (private set up by company) They do not like mobile connections from outside sources as this can create security breaches to their proprietary business applications.

An ADSL connection can be either wireless or wired only. It depends on the equipment being used...

Basically the ADSL modem could be just a modem or a combination modem/router(hardwired) or modem/wireless router. You will have to do a search on the models of the equipment to find out for sure....or contact the ISP to find out what it is that you have.

Would it be possible that the company would want me to have a wired router even if I have a wired dsl modem now? Would it make it more secure with both? I thought the wired dsl modem would be enough but I don't know...

I would think that the main reason for having stipulated a router (hardwired) is because most routers have built in hardware firewalls....instead of relying on the software type such as comes installed with windows! It is much safer than just being connected straight through to the internet from a modem!