Think of it like a plumbing problem. If you have a 1/2 inch pipe and try to use sink and shower at same time less pressure/less speed. Step it up to 3/4 inch pipe and volume/speed increases but still have less than if only one is being used. Now the internet is slightly different as you are looking at a page it is not downloading anything/using water. Only when you are watching a video or downloading large files are you constantly using the water/downloading. So if both computers are watching videos at the same time speed will be reduced. But if you are just surfing pages you will not notice much difference.
IP address is like your mailbox, when you are on the net you are assigned an IP address/mailbox. Sometimes if other computer logs on it will assign the same IP/mailbox to both, therefore a conflict. Shut one down and reboot and a new IP will be assigned. Very basic description, hope it helps.