"Source" is the engine that Half-Life 2 and the very popular Half-Life mod, Counter-Strike: Source, runs on. Valve has been working on the Source Engine for several years. This engine includes real-like physics.
Counter-Strike: Source and Half-Life 2 are run by the Source Engine.
Source is an extremely flexible/powerful video game engine developed by Valve Software, and it's primary use is for Half-Life 2, Counter-Strike: Source, and many Half-Life mods. But other games such as Vampires - Masqeurade: Bloodlines uses the same engine. It took Valve over 5 years of solid programming to develop Source.
(Also known as, a beast created solely based on better graphics/improved realism to satisfy newbs that like to cry on steampowered.com while destroying the game's competitive aspect.)