The Access Point Name (APN) defines a gateway between a mobile network and another computer network (usually the Internet). Quoting the linked Wikipedia article:
A mobile device making a data connection must be configured with an APN to present to the carrier. The carrier will then examine this identifier to determine what type of network connection should be created, for example: what IP addresses should be assigned to the wireless device, what security methods should be used, and how or if, it should be connected to some private customer network.
This configuration is usually found in Settings→Wireless & Networks→Mobile Networks→Access Points on your Android device.