Swift is a modern open source programming language that runs on macOS, Linux and on Windows.
Swift was developed initially by Apple to interoperate with their key frameworks, Cocoa and CocoaTouch, both of which are mostly implemented in Objective-C.
Swift is influenced by a large number of existing programming languages, and it incorporates concepts from a wide range of programming methods. Everything from scripting to object oriented and functional programming.
Apple refers to Swift as a "protocol oriented programming language" and has expressed the goal of eventually making Swift useful for everything from scripts to an operating system.
This Swift Tour is an introduction to the language on Apple's Public Developer Website.
Wikipedia's Swift Page giving a good, Wikipedia-styled overview.
Swift is documented in The Swift Programming Language. There is also a version on the iBooks Store. The ePub version is also available on Swift.org.