What is the technical term for this?

[Vod]

I have a laptop that doesn't have wifi.  I want to ethernet cable it to a router, then have the router connect to my existing wifi.

What term do I search for?  What feature should the router have?

It's been 15 years since my last network certification, and I can't remember. 

[NeuroticFish]

I think that's repeater. Or extender.
Just try a google for: connect router to wifi   
Good luck

[Vod]

I think that's repeater. Or extender.
Just try a google for: connect router to wifi   
Good luck

Yes, I tried searching for that, all I get is how to extend the wifi signal using a second router.  I don't want the second router to broadcast wifi, I want it to use the existing wifi.

[NeuroticFish]

On the 3rd page of results it's this.
http://www.cyberciti.biz/networking/howto-connect-two-wireless-router-wirelessly-bridge-with-open-source-software/
The image looks like what you'd need.
If I misunderstood then sorry.

[Vod]

On the 3rd page of results it's this.
http://www.cyberciti.biz/networking/howto-connect-two-wireless-router-wirelessly-bridge-with-open-source-software/
The image looks like what you'd need.
If I misunderstood then sorry.

That may do it!  Thanks for your help buddy!   

[Rannasha]

You don't need a router for it per se (a router has a bunch of extra functionality that's not needed for this purpose), an access point suffices.

On the AP that I use, this function is called "client mode".

edit: why not use a USB wifi dongle? Seems like a much simpler solution.