Router:
What is the purpose of a router?
A router is a device that assigns an IP address (your networking address) to your computers and then makes routing decisions based on that IP address! The router takes these IP addresses within the network and direct traffic from one device to another. For most home and small to medium sized offices their router usually includes a wireless access point built into the unit. This serves as an all-in-one device that handles your network traffic for both wired and wireless devices. A router also comes with a built-in switch that usually has four ports for wired devices.
Wireless Access Point:
What is the purpose of a wireless access point?
A wireless access point on the other hand serves as a wireless connection to the network without having the routing capabilities built into it. It is technically a smart antenna that can direct traffic to the router for proper IP address assignment. A wireless access point is an ideal purchase if the office already has a router equipped and wants to add a wireless network or extend it into another part of the building. Wireless access points also tend to much cheaper than an equivalent wireless router.
To sum it up nicely a router makes decisions and assigns IP addresses where as a wireless access point is an addition to a router that extends the reach of its wireless network. So if you need a network you need a router. If you already have a network but need it to reach further out you need a wireless access point!