A LATEX package is a file or collection of files containing extra commands and programming which add new formatting features, or modify those already existing. There over 6,000 packages, and over 5,000 of them are pre-installed with every full distribution of LATEX, ready to be used in your documents immediately.
Package files mostly end with the .sty filetype (some computers hide this, but it’s there) — they used to be called ‘style files’. Packages may also include other files as well, like fonts or configuration files.