API

An API (Application Programming Interface) is a set of features and rules that exist inside a software program (the application) enabling interaction with it through software - as opposed to a human user interface. The API can be seen as a simple contract (the interface) between the application offering it and other items, such as third party software or hardware.

In Web development, an API is generally a set of code features (e.g. methods, properties, events, and URLs) that a developer can use in their apps for interacting with components of a user's web browser, or other software/hardware on the user's computer, or third party websites and services.

For example:

The getUserMedia API can be used to grab audio and video from a user's webcam, which can then be used in any way the developer likes, for example, recording video and audio, broadcasting it to another user in a conference call, or capturing image stills from the video.
The Geolocation API can be used to retrieve location information from whatever service the user has available on their device (e.g. GPS), which can then be used in conjunction with the Google Maps APIs to for example plot the user's location on a custom map and show them what tourist attractions are in their area.
The Twitter APIs can be used to retrieve data from a user's twitter accounts, for example, to display their latest tweets on a web page.
The Web Animations API can be used to animate parts of a web page — for example, to make images move around or rotate.