when buying a laptop if it says wifi does this mean you dont need a router?

Answer 1

no, wifi means it has an internal wireless card, you will need to get a wireless router for home.

Answer 2

No.
It means you don't need to buy a WiFi adaptor for the laptop, it already has one built in.
You will be able to use it to join existing WiFi networks, access public hotspots, etc.

You will, however, still need a wireless router or access point if you want to create a wireless network of your own.

Answer 3

no, it means that the laptop has a wifi capacity. you still need an access point on your network, usually a wifi router