An Access Point is any additional wifi transmitter in your house that transmits the original signal. In my case, I use Powerline technology (that can transmit your internet signal over the house's own electrical wiring) to extend my signal. I have my primary wifi router connected to my cable modem in my study, and an Ethernet cable running from router to a Powerline adapter in a wall socket. This gets my internet signal into the electrical wiring, so I can plug another Powerline adapter into any electrical outlet and connect another Ethernet cable there to create an internet jack.
Instead of plugging a computer into that additional internet jack, I plugged in another wifi router, which I configured as an Access Point. All this router does is pick up the signal and transmit it via wifi.
There are 2 reasons why I did this convoluted connection: (1) the 2nd router that I'm using as an Access Point was supposed to function as an Extender as well, but it didn't function well, and (2) Extenders often cut down the speed of the data transmission.
You are correct that getting a new Wireless N router should give you more range.