What does a wireless adapter do?

Solution
A wireless adapter gives you wifi like on a laptop or your phone so you can just connect to your router over wifi instead of using an ethernet cable.

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Distinguished
A wifi adapter gives wifi capability. It can be USB or PCI that you install inside the case.

A repeater will extend a signal. If you buy a router it may have a repeater function. Place it half way between your router and computer to extend and boost the wifi signal in the house.